Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus AB : AP Calculus AB

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 #53 : Functions, Graphs, And Limits

Evaluate the following indefinite integral.

$\int e^xdx$

Possible Answers:

e^x+C

$\frac{1}{2}e^{-x}+C$

ln(x)+C

1/ln(x)+C

$e^{-x}+C$

Correct answer:

e^x+C

Explanation:

For this problem, we must simply remember that the integral of $e^{x}$ is $e^{x}$ , just like how the derivative of $e^{x}$ is $e^{x}$ . Just keep in mind that we need that constant of integration that would have been lost during differentiation.

Report an Error

Example Question #54 : Functions, Graphs, And Limits

Evaluate the following indefinite integral.

$\int 3y^2 dy$

Possible Answers:

y^3+C

$\frac{1}{3}y^3+C$

6y^3+C

$\frac{2}{3}y^3+C$

$\frac{3}{2}y^3+C$

Correct answer:

y^3+C

Explanation:

First, we know that we can pull the constant out of the integral, and we then evaluate the integral according to this equation:

$\int y^n dy=\frac{y^{n+1}}{n+1}+C, n\ne1$ . From this, we acquire the answer above. As a note, we cannot forget the constant of integration which would be lost during the differentiation.

Report an Error

Example Question #55 : Functions, Graphs, And Limits

$\int \sec x\tan x\ \mathrm{d}x=$

Possible Answers:

tan(x)sec(x)

$\frac{1}{2}sec^2xtanx +C$

-tan(x)+C

tan(x)+C

sec(x)+C

Correct answer:

sec(x)+C

Explanation:

The answer is sec(x)+C . The definition of the derivative of sec(x) is sec(x)tan(x) . Remember to add the to undefined integrals.

Report an Error

Example Question #261 : Ap Calculus Ab

Evaluate the integral:

$\int (x+2) dx$

Possible Answers:

x^2+2

$\frac{x^2}{2}+2x+C$

$\frac{x^2}{2}$

x^2+2x

Correct answer:

$\frac{x^2}{2}+2x+C$

Explanation:

In order to find the antiderivative, add 1 to the exponent and divide by the exponent.

$\frac{x^{1+1}}{2}+\frac{2x^{0+1}}{1}=\frac{x^2}{2}+2x$

Report an Error

Example Question #262 : Ap Calculus Ab

Evaluate:

$\int \frac{1}{x^4} dx$

Possible Answers:

$\frac{-5}{x^5}$

$\frac{-3}{x^3}$

$\frac{-1}{5x^5}$

$\frac{-1}{3x^3}$

Correct answer:

$\frac{-1}{3x^3}$

Explanation:

$\int x^{-4}= \frac{x^{-4+1}}{-3}= \frac{x^{-3}}{-3}=\frac{-1}{3x^3}$

Report an Error

Example Question #58 : Functions, Graphs, And Limits

Evaluate:

$\int (sin^2x*cosx) dx$

Possible Answers:

$(\frac{1}{3})sin^3x+C$

$\frac{sin^3x}{3}-\frac{cos^2x}{2}$

$\frac{cos^3x}{3}$

cos^3x

Correct answer:

$(\frac{1}{3})sin^3x+C$

Explanation:

You should first know that the derivative of sin(x)=cos(x) .

Therefore, looking at the equation you can see that the antiderivative should involve something close to: $\square sin^3x+C$

Now to figure out what value represents the square take the derivative of sin^3x and set it equal to what the original integral contained.

3sin^2x*cosx = sin^2x*cosx

Since the derivative of sin^3x contains a 3 that the integral does not show, we know that the square is equal to 1/3 . Thus, the answer is $\frac{1}{3}sin^3x+C$ .

Report an Error

Example Question #59 : Functions, Graphs, And Limits

Evaluate:

$\int cos(2x)dx$

Possible Answers:

-2sin(2x)

2sin(2x)

2cos(2x)

$(\frac{1}{2})sin(2x)+C$

$-\frac{1}{2}sin(2x)$

Correct answer:

$(\frac{1}{2})sin(2x)+C$

Explanation:

The antiderivative of cos(x) = sin(x) . The derivative of sin(2x) = 2cos(2x) . However, since there is no 2 in the original integral, we must divide sin(2x) by 2. Therefore, the answer is (1/2)sin(2x)+C.

Report an Error

Example Question #263 : Ap Calculus Ab

Evaluate the integral:

$\int (x^3-2x^2+5x-1) dx$

Possible Answers:

x^4-6x^3+10x^2-x +C

${4x^4}-6x^3+5x+C$

3x^2-4x+5+C

$\frac{x^4}{4}-\frac{2x^3}{3}+\frac{5x^2}{2}-x+C$

Correct answer:

$\frac{x^4}{4}-\frac{2x^3}{3}+\frac{5x^2}{2}-x+C$

Explanation:

When taking the antiderivative add one to the exponent and then divide by the exponent.

$\frac{x^{3+1}}{4}-\frac{2*x^{2+1}}{3}+\frac{5x^{1+1}}{2}-\frac{1*x^{0+1}}{1}$

$\frac{x^4}{4}-\frac{2x^3}{3}+\frac{5x^2}{2}-x+C$

Report an Error

Example Question #264 : Ap Calculus Ab

Evaluate the integral:

$\int (e^x)dx$

Possible Answers:

$\frac{e^{x^2}}{2}+C$

e^x +C

$e^{x^2}+C$

Cannot be evaluated

e^0

Correct answer:

e^x +C

Explanation:

The derivative of e^x=e^x . Therefore, the antiderivative of e^x is equal to itself.

Report an Error

Example Question #33 : Comparing Relative Magnitudes Of Functions And Their Rates Of Change

Evaluate:

$\int_{-4}^{4} (x^{9} + tan(x) - x^{3}cos(x))dx$

Possible Answers:

$5\pi$

Can't be determined from the information given.

Correct answer:

Explanation:

$f(x) = x^{9} + tan(x) - x^{3}cos(x)$ and

$f(-x) = (-x)^{9} + tan(-x) - (-x)^{3}cos(-x) =$

$-x^{9} - tan(x) + x^{3}(cos(x)) =$

$-[x^{9} + tan(x) - x^{3}(cos(x))] = -f(x)$

Recall that tan(x) is an odd function and cos(x) is an even function.

Thus, since f(x) is an odd function, the integral of this function from to will be zero.

Report an Error

View AP Calculus AB Tutors

Jeremy
Certified Tutor

University of Illinois at Chicago, Bachelor of Science, Physics.

View AP Calculus AB Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View AP Calculus AB Tutors

Christopher
Certified Tutor

University of Michigan-Ann Arbor, Bachelor of Science, Computer Science.

All AP Calculus AB Resources

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

Popular Subjects

Statistics Tutors in San Diego, Math Tutors in Miami, Chemistry Tutors in Dallas Fort Worth, Calculus Tutors in Atlanta, Physics Tutors in Dallas Fort Worth, English Tutors in Chicago, ACT Tutors in Seattle, Algebra Tutors in Seattle, Algebra Tutors in Houston, SSAT Tutors in Denver

Popular Courses & Classes

ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Seattle, SAT Courses & Classes in New York City, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Chicago, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Boston, LSAT Courses & Classes in Los Angeles

Popular Test Prep

SAT Test Prep in Miami, GMAT Test Prep in Washington DC, ACT Test Prep in Denver, LSAT Test Prep in Miami, ISEE Test Prep in Denver, MCAT Test Prep in Los Angeles, GRE Test Prep in Phoenix, SSAT Test Prep in Houston, LSAT Test Prep in Los Angeles, MCAT Test Prep in Boston

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 : AP Calculus AB

Study concepts, example questions & explanations for AP Calculus AB

All AP Calculus AB Resources

Example Questions

Example Question #53 : Functions, Graphs, And Limits

Example Question #54 : Functions, Graphs, And Limits

Example Question #55 : Functions, Graphs, And Limits

Example Question #261 : Ap Calculus Ab

Example Question #262 : Ap Calculus Ab

Example Question #58 : Functions, Graphs, And Limits

Example Question #59 : Functions, Graphs, And Limits

Example Question #263 : Ap Calculus Ab

Example Question #264 : Ap Calculus Ab

Example Question #33 : Comparing Relative Magnitudes Of Functions And Their Rates Of Change

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: