Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus BC : Volume of Cross Sections and Area of Region

Study concepts, example questions & explanations for AP Calculus BC

Create An Account

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #71 : Integrals

Find the area bound by the curve of g(t), the x and y axes, and the line $t=\frac{3 \pi}{4}$

g(t)=4sin(t)-6cos(t)

Possible Answers:

2.59

11.07

-2.59

-1.41

Correct answer:

2.59

Explanation:

Find the area bound by the curve of g(t), the x and y axes, and the line $t=\frac{3 \pi}{4}$

g(t)=4sin(t)-6cos(t)

We are asked to find the area under a curve. This sounds like a job for an integral.

We need to integrate our function from 0 to $t=\frac{3 \pi}{4}$ . These will be our limits of integration. With that in mind, our integral look like this.

$G(t)=\int_0^\frac{3\pi}{4}4sin(t)-6cos(t)dt$

Now, we need to recall the rules for integrating sine and cosine.

$1) \int sin(t)dt=-cos(t)+c$

$2) \int cos(t)dt=sin(t)+c$

With these rules in mind, we can integrate our original function to get:

$G(t)=\int_0^\frac{3\pi}{4}4sin(t)-6cos(t)dt=-4cos(t)-6sin(t)+c|_0^{\frac{3 \pi}{4}}$

$G(t)=-4cos(t)-6sin(t)+c|_0^{\frac{3 \pi}{4}}$

Now, we just need to evaluate our new function at the given limits. Let's start with 0

G(0)=-4cos(0)-6sin(0)+c=-4-0+c=-4+c

And our upper limit...

$G({\frac{3 \pi}{4}})=-4cos({\frac{3 \pi}{4}})-6sin({\frac{3 \pi}{4}})+c$

$-4cos({\frac{3 \pi}{4}})-6sin({\frac{3 \pi}{4}})+c=(-4)\frac{-\sqrt{2}}{2}-(6)\frac{-\sqrt{2}}{2}+c$

$(-4)\frac{-\sqrt{2}}{2}-(6)\frac{\sqrt{2}}{2}+c=2\sqrt{2}-3\sqrt{2}+c=-\sqrt{2}+c$

Now, we need to take the difference between our limits:

$G(\frac{3 \pi}{4})-G(0)=(-\sqrt{2}+c)-(-4+c)=-\sqrt{2}+4\approx2.585$

So, our answer is 2.59

Report an Error

← Previous 1 2 Next →

View AP Calculus BC Tutors

Ranjeeta
Certified Tutor

University of Rajasthan, Bachelor of Science, Mathematics. University of Rajasthan, Master of Science, Mathematics.

View AP Calculus BC Tutors

Magdy
Certified Tutor

Cairo University, Egypt, Bachelor of Science, Electrical Engineering. New Mexico State University-Main Campus, Doctor of Phil...

View AP Calculus BC Tutors

Yoonsik
Certified Tutor

Seoul National University, Bachelor of Science, Physics. University of Pennsylvania, Doctor of Philosophy, Atomic and Molecul...

All AP Calculus BC Resources

2 Diagnostic Tests 86 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in New York City, SSAT Tutors in Atlanta, Calculus Tutors in Phoenix, Biology Tutors in Phoenix, SSAT Tutors in New York City, MCAT Tutors in Miami, French Tutors in Denver, Biology Tutors in Denver, Spanish Tutors in Washington DC, Reading Tutors in Philadelphia

Popular Courses & Classes

LSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Chicago, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in Seattle, ISEE Courses & Classes in New York City, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Los Angeles, MCAT Test Prep in New York City, SAT Test Prep in Washington DC, SSAT Test Prep in Denver, MCAT Test Prep in Chicago, MCAT Test Prep in Atlanta, ISEE Test Prep in New York City, 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 BC : Volume of Cross Sections and Area of Region

Study concepts, example questions & explanations for AP Calculus BC

All AP Calculus BC Resources

Example Questions

Example Question #71 : Integrals

All AP Calculus BC Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: