We are open Saturday and Sunday!

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 #31 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Integrate:

$\int_{0}^{1}[x^2+\frac{x}{2}]dx$

Possible Answers:

$\frac{7}{12}$

$\frac{1}{12}$

Correct answer:

$\frac{7}{12}$

Explanation:

The integral of the function is equal to

$\int_{0}^{1}[x^2+\frac{x}{2}]dx= \frac{x^3}{3}+\frac{x^2}{4}\left.\begin{matrix} 1\\ 0 \end{matrix}\right|$

and was found using the following rule:

$\int x^ndx=\frac{x^{n+1}}{n+1}+C$

Finally, we evaluate by plugging in the upper bound into the resulting function and subtracting the resulting function with the lower bound plugged in:

$\frac{1}{3}+\frac{1}{4}-(0+0)=\frac{7}{12}$

Report an Error

Example Question #44 : Techniques Of Antidifferentiation

Solve:

$\int_{0}^{\pi} (x+\sin(x))dx$

Possible Answers:

$\frac{\pi^2}{2}-2$

$\frac{\pi^2}{2}+2$

$\frac{\pi^2}{2}$

Correct answer:

$\frac{\pi^2}{2}+2$

Explanation:

The integral is equal to

$\int_{0}^{\pi} (x+\sin(x))dx = \frac{x^2}{2}-\cos(x) \left.\begin{matrix} \pi \\0 \end{matrix}\right|$

The rules used to integrate are

$\int x^n dx = \frac{x^{n+1}}{n+1}+C$ , $\int \sin(x)dx = -\cos(x)+C$

Now, we solve by plugging in the upper bound of integration and then subtracting the result of plugging in the lower bound of integration:

$\frac{\pi^2}{2}-(-1)-(0-1)=\frac{\pi^2}{2}+2$

Report an Error

Example Question #661 : Ap Calculus Ab

Integrate:

$\int \frac{4}{3+x^2}dx$

Possible Answers:

$\frac{4}{\sqrt{3}}\arctan(\sqrt{3}x)+C$

$4\arctan(\frac{x}{\sqrt{3}})+C$

$\frac{1}{\sqrt{3}}\arctan(\frac{x}{\sqrt{3}})+C$

$\frac{4}{\sqrt{3}}\arctan(\frac{x}{\sqrt{3}})+C$

Correct answer:

$\frac{4}{\sqrt{3}}\arctan(\frac{x}{\sqrt{3}})+C$

Explanation:

The integral is equal to

$\frac{4}{\sqrt{3}}\arctan(\frac{x}{\sqrt{3}})+C$

and was found using the following rule:

$\int \frac{dx}{a^2+x^2} = \frac{1}{a}\arctan({\frac{x}{a}})+C$

Report an Error

Example Question #41 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Integrate:

$\int_{0}^{4}(x-x^2)dx$

Possible Answers:

$\frac{88}{3}$

$\frac{40}{3}$

$-\frac{40}{3}$

Correct answer:

$-\frac{40}{3}$

Explanation:

The integral is equal to

$\int_{0}^{4}(x-x^2)dx = \frac{x^2}{2}-\frac{x^3}{3}\left.\begin{matrix} 4\\0 \end{matrix}\right|$

The following rule was used to integrate:

$\int x^n dx=\frac{x^{n+1}}{n+1}+C$

Now, we find the numerical answer by plugging in the upper bound of integration and subtracting what we get from plugging in the lower bound of integration:

$8-\frac{64}{3}-(0-0)=-\frac{40}{3}$

Report an Error

Example Question #41 : Techniques Of Antidifferentiation

Integrate:

$\int_{0}^{2\pi}5\sec^2(x)dx$

Possible Answers:

$\pi$

Undefined

Correct answer:

Explanation:

The integral is equal to

$\int_{0}^{2\pi}5\sec^2(x)dx=5\tan(x)\left.\begin{matrix} 2\pi\\0 \end{matrix}\right|$

and was found using the identical rule.

Evaluating by plugging in the upper bound and subtracting from what we get from plugging in the lower bound, we get

$5(0)-(5 \cdot 0)=0$

Report an Error

Example Question #1 : Fundamental Theorem Of Calculus

Wolframalpha--plot_piecewisexxlt03-x0ltxlt213-xxgt2--2013-09-10_1008

Find $\lim _{x\rightarrow 0}f(x)$

Possible Answers:

$+\infty$

Does not exist

Correct answer:

Does not exist

Explanation:

The one side limits are not equal: left is 0 and right is 3

Report an Error

Example Question #2 : Fundamental Theorem Of Calculus

Wolframalpha--plot_piecewisexxlt03-x0ltxlt213-xxgt2--2013-09-10_1008

Which of the following is a vertical asymptote?

Possible Answers:

y=0

x=0

y=3

x=3

Correct answer:

x=3

Explanation:

When approaches 3, approaches $\pm \infty$ .

Vertical asymptotes occur at values. The horizontal asymptote occurs at

y=0 .

Report an Error

Example Question #3 : Fundamental Theorem Of Calculus

$f(x) = \frac{x+1}{\sqrt{x^2 -4}}$

What are the horizontal asymptotes of f(x) ?

Possible Answers:

y=1

x=1

x=0

x=-1

y=0

Correct answer:

y=1

Explanation:

Compute the limits of f(x) as approaches infinity.

Report an Error

Example Question #4 : Fundamental Theorem Of Calculus

Write the domain of the function.

$f(x)=\frac{(x^{4}-81)^{1/2}}{x-4}$

Possible Answers:

$x\neq -9\ and\ x\neq 9$

$x\neq 4\ and\ x\neq 3$

${x\neq 4}$

$x\neq 4\ and\ \left | x \right |\geq 3$

$x\geq 4\ and\ x\neq 3$

Correct answer:

$x\neq 4\ and\ \left | x \right |\geq 3$

Explanation:

The answer is ${x\mid x\neq 4\ and\ \left | x \right |\geq 3}$

The denominator must not equal zero and anything under a radical must be a nonnegative number.

Report an Error

Example Question #5 : Fundamental Theorem Of Calculus

What is the value of the derivative of $f(x)=x^3+6x^2+\frac{3}{4}x$ at x=1?

Possible Answers:

$\frac{61}{4}$

$\frac{63}{4}$

$\frac{15}{4}$

Correct answer:

$\frac{63}{4}$

Explanation:

First, find the derivative of the function, which is:

$f{}'(x)=3x^2+12x+\frac{3}{4}$

Then, plug in 1 for x:

$3(1^2)+12(1)+\frac{3}{4}$

The result is $\frac{63}{4}$ .

Report an Error

View AP Calculus AB Tutors

Dalton
Certified Tutor

University of Massachusetts Amherst, Doctor of Philosophy, Mathematics.

View AP Calculus AB Tutors

Colton
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Mathematics.

View AP Calculus AB Tutors

Rachel
Certified Tutor

University of Arkansas at Little Rock, Bachelor in Arts, Mathematics.

All AP Calculus AB Resources

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

Popular Subjects

French Tutors in Atlanta, SSAT Tutors in New York City, Biology Tutors in San Diego, Reading Tutors in Atlanta, SAT Tutors in Phoenix, GMAT Tutors in Los Angeles, GRE Tutors in Denver, ACT Tutors in San Francisco-Bay Area, Biology Tutors in San Francisco-Bay Area, Math Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in San Diego, ACT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Washington DC, GMAT Courses & Classes in Seattle, SSAT Courses & Classes in Washington DC, SSAT Courses & Classes in Houston, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in New York City, SSAT Courses & Classes in Miami, ISEE Courses & Classes in Miami

Popular Test Prep

SAT Test Prep in Houston, MCAT Test Prep in New York City, GRE Test Prep in Seattle, GRE Test Prep in Denver, ISEE Test Prep in Phoenix, SAT Test Prep in San Diego, LSAT Test Prep in Philadelphia, MCAT Test Prep in Philadelphia, LSAT Test Prep in San Diego, SSAT Test Prep in New York City

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 #31 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #44 : Techniques Of Antidifferentiation

Example Question #661 : Ap Calculus Ab

Example Question #41 : Antiderivatives Following Directly From Derivatives Of Basic Functions

Example Question #41 : Techniques Of Antidifferentiation

Example Question #1 : Fundamental Theorem Of Calculus

Example Question #2 : Fundamental Theorem Of Calculus

Example Question #3 : Fundamental Theorem Of Calculus

Example Question #4 : Fundamental Theorem Of Calculus

Example Question #5 : Fundamental Theorem Of Calculus

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: