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 #127 : Definite Integrals

$\int_{0}^{2}t^{\frac{3}{2}}dt$

Possible Answers:

$\frac{2}{5}(2^{\frac{4}{5}})+C$

$\frac{2}{5}(2^{\frac{5}{2}})+C$

$\frac{2}{5}(2^{\frac{2}{5}})$

$\frac{1}{5}(2^{\frac{2}{5}})+C$

$\frac{2}{7}(2^{\frac{2}{5}})+C$

Correct answer:

$\frac{2}{5}(2^{\frac{5}{2}})+C$

Explanation:

First, integrate this expression. Remember to raise the exponent by 1 and then also put that result on the denominator:

$\frac{t^{\frac{5}{2}}}{\frac{5}{2}}$

Simplify to get:

$\frac{2}{5}t^{\frac{5}{2}}$

Now, evaluate at 2 and then 0. Subtract the results:

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

Now, add a C because it is an indefinite integral:
$\frac{2}{5}(2^{\frac{2}{5}})+C$

Report an Error

Example Question #128 : Definite Integrals

If f{}'(x)=2x+1 and f(1)=3 , what is the original f(x) function?

Possible Answers:

f(x)=2x^2+x+1

f(x)=x^2+x-1

f(x)=x^2-x+1

f(x)=x^2+x+1

f(x)=x^2+x

Correct answer:

f(x)=x^2+x+1

Explanation:

First, set up the integral expression:

$\int 2x+1dx$

Now, integrate. Remember to raise the exponent by 1 and then put that result on the denominator:

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

Plug in your initial conditions to find C:

1^2+1+C=3; C=1

Now plug back in to get your initial f(x) function:

f(x)=x^2+x+1

Report an Error

Example Question #129 : Definite Integrals

Evaluate.

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

Possible Answers:

$\frac{1}{5}$

$\frac{9}{8}$

$\frac{2}{3}$

$\frac{5}{7}$

Answer not listed.

Correct answer:

Answer not listed.

Explanation:

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

In this case, $f(x) = \frac{1}{2} x$ .

The antiderivative is $F(x) = \frac{1}{4} x^2$ .

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

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

$= \frac{1}{4} (2)^2 - \left ( \frac{1}{4} (1)^2 \right )$

$= \frac{3}{4}$

Report an Error

Example Question #130 : Definite Integrals

Evaluate.

$\int_{12}^{14} e^ {x -7}\ dx$

Possible Answers:

Answer not listed.

573.8

948.2

1,579.4

232.4

Correct answer:

948.2

Explanation:

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

In this case, $f(x) = e^ {x -7}$ .

The antiderivative is $F(x) = e^ {x -7}$ .

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

$\int_{12}^{14} e^ {x -7}\ dx = \left (e^ {x -7} \right )_{12}^{14}$

$= e^ {14 -7} - \left ( e^ {12 -7} \right )$

= 948.2

Report an Error

Example Question #131 : Definite Integrals

Evaluate.

$\int_{6}^{7} \frac{x-4}{x-5} \ dx$

Possible Answers:

45.2

Answer not listed.

18.3

16.7

3.5

Correct answer:

Answer not listed.

Explanation:

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

In this case, $f(x) =\frac{x-4}{x-5}$ .

The antiderivative is $F(x) =\ln(x-5) + x$ .

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

$\int_{6}^{7} \frac{x-4}{x-5} \ dx = \left (\ln(x-5) + x \right )_{6}^{7}$

$= \ln(7-5) + 7 - \left ( \ln(6-5) + 6 \right )$

= 13.7

Report an Error

Example Question #132 : Definite Integrals

Evaluate.

$\int_{0}^{1} \cos(2x-9) \ dx$

Possible Answers:

-4.2

1.54

3.8

0.02

Answer not listed.

Correct answer:

0.02

Explanation:

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

In this case, $f(x) = \cos(2x-9)$ .

The antiderivative is $F(x) = \frac{\sin(2x-9)}{2}$ .

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

$\int_{0}^{1} \cos(2x-9) \ dx = \left ( \frac{\sin(2x-9)}{2} \right )_{0}^{1}$

$= \frac{\sin(2(1)-9)}{2} - \left ( \frac{\sin(2(0)-9)}{2} \right )$

= 0.02

Report an Error

Example Question #133 : Definite Integrals

Evaluate.

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

Possible Answers:

2.04

Answer not listed.

1.38

-2.03

-0.06

Correct answer:

-0.06

Explanation:

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

In this case, $f(x) = -\frac{\sin(2x)}{2}$ .

The antiderivative is $F(x) = \frac{\cos(2x)}{4}$ .

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

$\int_{1}^{2} -\frac{\sin(2x)}{2} \ dx= \left ( \frac{\cos(2x)}{4} \right )_{1}^{2}$

$= \frac{\cos(2(2))}{4} - \left ( \frac{\cos(2(1))}{4} \right )$

= -0.06

Report an Error

Example Question #134 : Definite Integrals

Evaluate.

$\int_{2}^{3}\sec^2 (12x-1)\ dx$

Possible Answers:

Answer not listed.

2.74

4.26

0.94

0.02

Correct answer:

0.02

Explanation:

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

In this case, $f(x) =\sec^2 (12x-1)$ .

The antiderivative is $F(x) = \frac{\tan(12x-1)}{12}$ .

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

$\int_{2}^{3}\sec^2 (12x-1)\ dx = \left ( \frac{\tan(12x-1)}{12} \right )_{2}^{3}$

$= \frac{\tan(12(3)-1)}{12} - \left ( \frac{\tan(12(2)-1)}{12} \right )$

= 0.02

Report an Error

Example Question #135 : Definite Integrals

$\int_{0}^{2}x^3+4x^2-x+1dx$

Possible Answers:

$\frac{41}{3}$

$\frac{38}{3}$

$\frac{50}{3}$

$\frac{43}{3}$

$\frac{44}{3}$

Correct answer:

$\frac{44}{3}$

Explanation:

First, integrate this expression. Remember to raise the exponent by 1 and then put that result on the denominator:

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

Now, evaluate at 2 and then 0. Subtract the results:
$(\frac{16}{4}+\frac{32}{3}-\frac{4}{2}+2)-0=4+\frac{32}{3}-2+2=\frac{44}{3}$

Report an Error

Example Question #136 : Definite Integrals

$\int_{1}^{2}x^{\frac{3}{4}}dx$

Possible Answers:

3.5069

1.8058

2.3456

1.2950

1.3506

Correct answer:

1.3506

Explanation:

First, integrate this expression. Remember to add one to the exponent and then also put that result on the denominator:

$\frac{x^{\frac{7}{4}}}{\frac{7}{4}}$

Simplify:

$\frac{4}{7}(x^{\frac{7}{4}})$

Evaluate at 2 and then 1. Subtract the results:

$(\frac{4}{7}(2^{\frac{7}{4}}))-(\frac{4}{7}(1^{\frac{7}{4}}))$

Round to four places:

1.9220-.5714=1.3506

Report an Error

View Calculus 2 Tutors

Ainsley
Certified Tutor

Rice University, Bachelor of Science, Physics.

View Calculus 2 Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

View Calculus 2 Tutors

Timothy
Certified Tutor

Bethune-Cookman University, Bachelor of Science, Mathematics. University of Phoenix, Master of Science, Computer and Informat...

All Calculus 2 Resources

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

Popular Subjects

SAT Tutors in Philadelphia, ACT Tutors in San Francisco-Bay Area, GRE Tutors in Dallas Fort Worth, MCAT Tutors in Houston, Computer Science Tutors in Los Angeles, LSAT Tutors in Dallas Fort Worth, GRE Tutors in Denver, Statistics Tutors in San Diego, GRE Tutors in Seattle, Calculus Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Chicago, ACT Courses & Classes in Miami, GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in Boston, ACT Courses & Classes in Houston, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Houston, LSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Atlanta, ISEE Test Prep in Miami, MCAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, MCAT Test Prep in Washington DC, SSAT Test Prep in Los Angeles, GRE Test Prep in Chicago, SAT Test Prep in Seattle, SAT Test Prep in Washington DC, ISEE Test Prep in Los Angeles

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 #127 : Definite Integrals

Example Question #128 : Definite Integrals

Example Question #129 : Definite Integrals

Example Question #130 : Definite Integrals

Example Question #131 : Definite Integrals

Example Question #132 : Definite Integrals

Example Question #133 : Definite Integrals

Example Question #134 : Definite Integrals

Example Question #135 : Definite Integrals

Example Question #136 : Definite Integrals

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: