Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Finding Integrals

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #27 : Definite Integrals

Find the area between y=sin(x) and y=sec^2(x) between $x:(0, \frac{\pi}{4})$

Possible Answers:

$\frac{\sqrt2}{2}+2$

$\frac{\sqrt2}{2}$

Correct answer:

$\frac{\sqrt2}{2}$

Explanation:

We can write this problem as:

$\int_{0}^{\frac{\pi}{4}}(sec^2(x)-sin(x))dx$

Integrating:

$\int(sec^2(x)-sin(x))dx=tan(x)+cos(x)+C=F(x)$

By the fundamental theorem of calculus:

$\int_{0}^{\frac{\pi}{4}}(sec^2(x)-sin(x))dx=F(\frac{\pi}{4})-F(0)$

$=[tan(\frac{\pi}{4})+cos(\frac{\pi}{4})]-[tan(0)+cos(0)]=[1+\frac{\sqrt2}{2}]-[1]$

$\int_{0}^{\frac{\pi}{4}}(sec^2(x)-sin(x))dx=\frac{\sqrt2}{2}$

Report an Error

Example Question #28 : Definite Integrals

$Evaluate:\int_{0}^{5}(x^2+x)dx$

Possible Answers:

$\frac{325}{2}$

$\frac{325}{6}$

$\frac{175}{6}$

$\frac{200}{6}$

$\frac{250}{3}$

Correct answer:

$\frac{325}{6}$

Explanation:

Compute the Indefinite Integral

$\int (x^2+x)dx=\frac{x^3}{3}+\frac{x^2}{2}$

Evaluate the integral

$(\frac{5^3}{3}+\frac{5^2}{2})-(\frac{0^3}{3}+\frac{0^2}{2})$

$(\frac{125}{3}+\frac{25}{2})-(0+0)$

$\frac{250}{6}+\frac{75}{6}=\frac{325}{6}$

Report an Error

Example Question #29 : Definite Integrals

Suppose u=ax , where is a constant

Find such that $\int_{0}^{2} 5u dx =2$

Possible Answers:

u=5x

$u=\frac{1}{5}x$

$u=\frac{5}{2}x$

u=x

Correct answer:

$u=\frac{1}{5}x$

Explanation:

$\int 5ax dx= \frac{5}{2}ax^2 +C= F(x)$

By the fundamental theorem of calculus:

$\int_{0}^{2} 5u dx =F(2)-F(0)=2$

$\frac{5}{2}a*2^2-0=2$

10a=2

$a=\frac{1}{5}$

$u=\frac{1}{5}x$

Report an Error

Example Question #30 : Definite Integrals

Evaluate this integral.

$\int_{2}^{0} 3+4x dx$

Possible Answers:

Answer not listed

Correct answer:

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, f(x) = 3 + 4x .

The antiderivative is F(x) = 3x + 2x^2 .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{2}^{0} 3 + 4x dx = \left (3x + 2x^2 \right ) _{2}^{0}$

$= 3(0) + 2(0)^2 - \left (3(2) + 2(2)^2 \right )$

= - 14

Report an Error

Example Question #31 : Definite Integrals

Evaluate this integral.

$\int_{1}^{2} e^x dx$

Possible Answers:

9.43

-6.48

4.67

2.16

Answer not listed

Correct answer:

4.67

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, f(x) = e^x .

The antiderivative is F(x) = e^x .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{1}^{2} e^x dx = \left (e^x \right ) _{1}^{2}$

$= e^{2} - e^{1}$

= 4.67

Report an Error

Example Question #32 : Definite Integrals

Evaluate this integral.

$\int_{1}^{2} 16x^3 - \frac{1}{x} dx$

Possible Answers:

64.8

Answer not listed

59.3

12.5

98.4

Correct answer:

59.3

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, $f(x) = 16x^3 - \frac{1}{x}$ .

The antiderivative is F(x) =4x^4 - ln(x) .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{1}^{2} 16x^3 - \frac{1}{x} dx = \left (4x^4 - ln(x) \right ) _{1}^{2}$

$= 4(2)^4 - ln(2) - \left (4(1)^4 - ln(1) \right )$

= 59.3

Report an Error

Example Question #33 : Definite Integrals

Evaluate this integral.

$\int_{0}^{2} x^2 dx$

Possible Answers:

$\frac{7}{8}$

$\frac{8}{3}$

$\frac{3}{2}$

Answer not listed

$\frac{4}{5}$

Correct answer:

$\frac{8}{3}$

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, f(x) = x^2 .

The antiderivative is $F(x) = \frac{1}{3}x^3$ .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{0}^{2} x^2 dx = \left ( \frac{1}{3}x^3 \right )_{0}^{2}$

$= \frac{1}{3}(2)^3 - \left ( \frac{1}{3}(0)^3 \right )$

$= \frac{8}{3}$

Report an Error

Example Question #34 : Definite Integrals

Evaluate this integral.

$\int_{0}^{2} x-5} dx$

Possible Answers:

Answer not listed

Correct answer:

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, f(x) = x-5 .

The antiderivative is $F(x) = \frac{1}{2}x^2 - 5x$ .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{0}^{2} x-5 dx = \left ( \frac{1}{2}x^2 - 5x \right )_{0}^{2}$

$= \frac{1}{2}(2)^2 - 5(2) - \left (\frac{1}{2}(0)^2 - 5(0) \right )$

= -8

Report an Error

Example Question #35 : Definite Integrals

Evaluate this integral.

$\int_{1}^{2} 12x - 1 \ dx$

Possible Answers:

Answer not listed

Correct answer:

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, f(x) = 12x -1 .

The antiderivative is F(x) = 6x^2 - x .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{1}^{2} x-5 \ dx = \left ( 6x^2 - x \right )_{1}^{2}$

$= 6(2)^2 - (2) - \left ( 6(1)^2 - (1)\right )$

= 17

Report an Error

Example Question #36 : Definite Integrals

Evaluate this integral.

$\int_{0}^{\pi} \sin x \ dx$

Possible Answers:

$\pi$

Answer not listed

Correct answer:

Explanation:

$\int_{a}^{b} f(x) dx$

In order to evaluate this integral, first find the antiderivative of f(x).

In this case, $f(x) = \sin x$ .

The antiderivative is $F(x) = -\cos x$ .

Using the Fundamental Theorem of Calculus, evaluate the integral using the antiderivative:

$\int_{0}^{\pi} \sin x\ dx = \left ( -\cos x \right )_{0}^{\pi}$

$= -\cos (\pi) - \left (-\cos (0) \right )$

= 2

Report an Error

View Calculus 2 Tutors

Jasmine
Certified Tutor

Mercer University, Bachelor of Science, Biochemistry. Mercer University, Master of Science, Biomedical Sciences.

View Calculus 2 Tutors

Ping
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science. University of North Texas, Master of Arts, Education.

View Calculus 2 Tutors

Kelli
Certified Tutor

Middle Tennessee State University, Bachelor, Recording Industry. North Carolina State University, Doctorate (PhD), Mathematic...

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Chicago, Biology Tutors in Boston, Chemistry Tutors in Dallas Fort Worth, MCAT Tutors in Los Angeles, GMAT Tutors in Denver, LSAT Tutors in San Diego, Computer Science Tutors in San Francisco-Bay Area, French Tutors in Phoenix, SSAT Tutors in San Francisco-Bay Area, Calculus Tutors in Denver

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, GRE Courses & Classes in Philadelphia, ISEE Courses & Classes in Atlanta, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Chicago, ACT Courses & Classes in New York City, SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Boston, LSAT Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in New York City, GMAT Test Prep in San Diego, GRE Test Prep in New York City, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in San Francisco-Bay Area, GRE Test Prep in Atlanta, SAT Test Prep in Atlanta, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Boston, SSAT Test Prep in Washington DC

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

Calculus 2 : Finding Integrals

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #27 : Definite Integrals

Example Question #28 : Definite Integrals

Example Question #29 : Definite Integrals

Example Question #30 : Definite Integrals

Example Question #31 : Definite Integrals

Example Question #32 : Definite Integrals

Example Question #33 : Definite Integrals

Example Question #34 : Definite Integrals

Example Question #35 : Definite Integrals

Example Question #36 : Definite Integrals

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: