Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus AB : Techniques of antidifferentiation

Study concepts, example questions & explanations for AP Calculus AB

Create An Account

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Antiderivatives Following Directly From Derivatives Of Basic Functions

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{27}^{31}(\frac{(8x)}{51})dx\end{align*}$

Possible Answers:

7.00

2.19

100.08

18.20

Correct answer:

18.20

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int x^{a}=\frac{x^{a+1}}{a+1}\\&\int_{27}^{31}(\frac{(8x)}{51})dx=\frac{(4x^{2})}{51}|_{27}^{31}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{27}^{31}(\frac{(8x)}{51})dx=\frac{(4(31)^{2})}{51}-(\frac{(4(27)^{2})}{51})\\&\int_{27}^{31}(\frac{(8x)}{51})dx=18.20\end{align*}$

Report an Error

Example Question #3 : Antiderivatives Following Directly From Derivatives Of Basic Functions

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{-6}^{-3}(\frac{(10\cdot 2^{(\frac{x}{4})})}{7})dx\end{align*}$

Possible Answers:

1.99

0.34

0.64

0.24

Correct answer:

1.99

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[b^{ax}]=\frac{b^{ax}}{aln(b)}\\&\int_{-6}^{-3}(\frac{(10\cdot 2^{(\frac{x}{4})})}{7})dx=\frac{(40\cdot 2^{(\frac{x}{4})})}{(7ln(2))}|_{-6}^{-3}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{-6}^{-3}(\frac{(10\cdot 2^{(\frac{x}{4})})}{7})dx=\frac{(40\cdot 2^{(\frac{(-3)}{4})})}{(7ln(2))}-(\frac{(40\cdot 2^{(\frac{(-6)}{4})})}{(7ln(2))})\\&\int_{-6}^{-3}(\frac{(10\cdot 2^{(\frac{x}{4})})}{7})dx=1.99\end{align*}$

Report an Error

Example Question #4 : Antiderivatives Following Directly From Derivatives Of Basic Functions

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{-24}^{-19}(\frac{59}{(9x)})dx\end{align*}$

Possible Answers:

-10.41

-0.16

-5.21

-1.53

Correct answer:

-1.53

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int\frac{a}{u}=aln(u)=ln(u^{a})\\&\int_{-24}^{-19}(\frac{59}{(9x)})dx=\frac{(59ln(x))}{9}|_{-24}^{-19}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{-24}^{-19}(\frac{59}{(9x)})dx=\frac{(59ln((-19)))}{9}-(\frac{(59ln((-24)))}{9})\\&\int_{-24}^{-19}(\frac{59}{(9x)})dx=-1.53\end{align*}$

Report an Error

Example Question #5 : Antiderivatives Following Directly From Derivatives Of Basic Functions

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{-6}^{-2}(\frac{11}{59})dx\end{align*}$

Possible Answers:

6.71

0.20

0.11

0.75

Correct answer:

0.75

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int x^{a}=\frac{x^{a+1}}{a+1}\\&\int_{-6}^{-2}(\frac{11}{59})dx=\frac{(11x)}{59}|_{-6}^{-2}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{-6}^{-2}(\frac{11}{59})dx=\frac{(11(-2))}{59}-(\frac{(11(-6))}{59})\\&\int_{-6}^{-2}(\frac{11}{59})dx=0.75\end{align*}$

Report an Error

Example Question #6 : Antiderivatives Following Directly From Derivatives Of Basic Functions

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{-16}^{-14}(\frac{(9cos(x + 2))}{11})dx\end{align*}$

Possible Answers:

3.50

8.25

0.15

1.25

Correct answer:

1.25

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[cos(ax)]=\frac{sin(ax)}{a}\\&\int_{-16}^{-14}(\frac{(9cos(x + 2))}{11})dx=\frac{(9sin(x + 2))}{11}|_{-16}^{-14}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{-16}^{-14}(\frac{(9cos(x + 2))}{11})dx=\frac{(9sin((-14) + 2))}{11}-(\frac{(9sin((-16) + 2))}{11})\\&\int_{-16}^{-14}(\frac{(9cos(x + 2))}{11})dx=1.25\end{align*}$

Report an Error

Example Question #11 : Techniques Of Antidifferentiation

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{-6}^{-2.5}(10e^{(x)})dx\end{align*}$

Possible Answers:

0.23

6.61

0.80

0.14

Correct answer:

0.80

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[e^{ax}]=\frac{e^{ax}}{a}\\&\int_{-6}^{-2.5}(10e^{(x)})dx=10e^{(x)}|_{-6}^{-2.5}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{-6}^{-2.5}(10e^{(x)})dx=10e^{((-2.5))}-(10e^{((-6))})\\&\int_{-6}^{-2.5}(10e^{(x)})dx=0.80\end{align*}$

Report an Error

Example Question #11 : Techniques Of Antidifferentiation

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{7.5}^{12.5}(\frac{3^{(\frac{x}{3})}}{4})dx\end{align*}$

Possible Answers:

55.77

223.07

340.17

540.93

Correct answer:

55.77

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[b^{ax}]=\frac{b^{ax}}{aln(b)}\\&\int_{7.5}^{12.5}(\frac{3^{(\frac{x}{3})}}{4})dx=\frac{(3\cdot 3^{(\frac{x}{3})})}{(4ln(3))}|_{7.5}^{12.5}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{7.5}^{12.5}(\frac{3^{(\frac{x}{3})}}{4})dx=\frac{(3\cdot 3^{(\frac{(12.5)}{3})})}{(4ln(3))}-(\frac{(3\cdot 3^{(\frac{(7.5)}{3})})}{(4ln(3))})\\&\int_{7.5}^{12.5}(\frac{3^{(\frac{x}{3})}}{4})dx=55.77\end{align*}$

Report an Error

Example Question #633 : Ap Calculus Ab

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{14}^{15}(\frac{2^{(\frac{x}{3})}}{20})dx\end{align*}$

Possible Answers:

1.43

0.16

0.24

3.00

Correct answer:

1.43

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[b^{ax}]=\frac{b^{ax}}{aln(b)}\\&\int_{14}^{15}(\frac{2^{(\frac{x}{3})}}{20})dx=\frac{(3\cdot 2^{(\frac{x}{3})})}{(20ln(2))}|_{14}^{15}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{14}^{15}(\frac{2^{(\frac{x}{3})}}{20})dx=\frac{(3\cdot 2^{(\frac{(15)}{3})})}{(20ln(2))}-(\frac{(3\cdot 2^{(\frac{(14)}{3})})}{(20ln(2))})\\&\int_{14}^{15}(\frac{2^{(\frac{x}{3})}}{20})dx=1.43\end{align*}$

Report an Error

Example Question #634 : Ap Calculus Ab

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{9}^{12.5}(\frac{(20cos(3x))}{3})dx\end{align*}$

Possible Answers:

-2.56

-20.52

-5.64

-0.42

Correct answer:

-2.56

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int[cos(ax)]=\frac{sin(ax)}{a}\\&\int_{9}^{12.5}(\frac{(20cos(3x))}{3})dx=\frac{(20sin(3x))}{9}|_{9}^{12.5}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{9}^{12.5}(\frac{(20cos(3x))}{3})dx=\frac{(20sin(3(12.5)))}{9}-(\frac{(20sin(3(9)))}{9})\\&\int_{9}^{12.5}(\frac{(20cos(3x))}{3})dx=-2.56\end{align*}$

Report an Error

Example Question #635 : Ap Calculus Ab

$\begin{align*}&\text{Evaluate the integral: }\\&\int_{10}^{15}(\frac{51}{(2x)})dx\end{align*}$

Possible Answers:

55.83

10.34

1.26

36.19

Correct answer:

10.34

Explanation:

$\begin{align*}&\text{In performing an integral, familiarity with derivative rules}\\&\text{can prove useful. After all, an integral is essentially the}\\&\text{opposite operation of a derivative. Consider how in a derivative}\\&\text{we’d use the chain rule to multiply the derivative of the “inside”}\\&\text{of a function by the derivative of the outside? Integrals, in}\\&\text{similar fashion, entail a division.}\\&\text{Utilizing integral rules:}\\&\int x^{a}=\frac{x^{a+1}}{a+1}\\&\int_{10}^{15}(\frac{51}{(2x)})dx=\frac{(51ln(x))}{2}|_{10}^{15}\\&\text{Now we just subtract the function value at the lower bound from that of the upper bound:}\\&\int_{10}^{15}(\frac{51}{(2x)})dx=\frac{(51ln((15)))}{2}-(\frac{(51ln((10)))}{2})\\&\int_{10}^{15}(\frac{51}{(2x)})dx=10.34\end{align*}$

Report an Error

View AP Calculus AB Tutors

Aaron
Certified Tutor

Tulsa Community College, Associate in Science, Mechanical Engineering.

View AP Calculus AB Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View AP Calculus AB Tutors

Jody
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Mathematics.

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Los Angeles, Spanish Tutors in Washington DC, Biology Tutors in Los Angeles, SAT Tutors in Atlanta, English Tutors in Seattle, Math Tutors in San Diego, Statistics Tutors in San Francisco-Bay Area, Calculus Tutors in Washington DC, SAT Tutors in San Francisco-Bay Area, Chemistry Tutors in Washington DC

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Boston, SSAT Courses & Classes in Boston, ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in New York City, SSAT Courses & Classes in Chicago, Spanish Courses & Classes in Chicago, LSAT Courses & Classes in New York City, ACT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SAT Test Prep in Boston, ISEE Test Prep in Los Angeles, ISEE Test Prep in Atlanta, ISEE Test Prep in Philadelphia, SSAT Test Prep in Seattle, LSAT Test Prep in Miami, LSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Philadelphia, GMAT Test Prep in New York City, SAT Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

AP Calculus AB : Techniques of antidifferentiation

Study concepts, example questions & explanations for AP Calculus AB

All AP Calculus AB Resources

Example Questions

Example Question #2 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #3 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #4 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #5 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #6 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #11 : Techniques Of Antidifferentiation

Example Question #11 : Techniques Of Antidifferentiation

Example Question #633 : Ap Calculus Ab

Example Question #634 : Ap Calculus Ab

Example Question #635 : Ap Calculus Ab

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: