Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Definite 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 #184 : Finding Integrals

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

Possible Answers:

$\frac{51}{8}$

$\frac{51}{4}$

$\frac{39}{2}$

$\frac{51}{2}$

$\frac{53}{2}$

Correct answer:

$\frac{51}{2}$

Explanation:

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

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

Now, evaluate at 4 and then 1. Subtract the results:

$(\frac{64}{3}-8+16)-(\frac{1}{3}-\frac{1}{2}+4)$

Simplify to get your answer:

$4+\frac{129}{6}=\frac{51}{2}$

Report an Error

Example Question #171 : Definite Integrals

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

Possible Answers:

$\frac{31}{5}$

$\frac{32}{3}$

$\frac{36}{5}$

$\frac{32}{9}$

$\frac{32}{5}$

Correct answer:

$\frac{32}{5}$

Explanation:

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

$\frac{x^5}{5}+\frac{x^2}{2}-x$

Evaluate at 2 and then 0. Subtract the results:

$(\frac{32}{5}+2-2)-0=\frac{32}{5}$

Report an Error

Example Question #186 : Finding Integrals

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

Possible Answers:

$\frac{19}{3}$

$\frac{20}{3}$

$\frac{17}{3}$

$\frac{16}{3}$

$\frac{19}{4}$

Correct answer:

$\frac{19}{3}$

Explanation:

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

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

Now, evaluate at 2 and then at 1. Subtract the results:

$(\frac{32}{3}-6)-(\frac{4}{3}-3)$

Simplify to get your answer:

$\frac{28}{3}-3=\frac{19}{3}$

Report an Error

Example Question #174 : Definite Integrals

$\int_{1}^{3} 3x^4+7x+3$

Possible Answers:

180

177

$-\frac {896}{5}$

$\frac {896}{5}$

Correct answer:

$\frac {896}{5}$

Explanation:

Step 1: Integrate:

$\int_{1}^{3}3x^4+7x+3\rightarrow \frac {3x^5}{5}+\frac {7x^2}{2}+3x|_{1}^{3}$

Step 2: Evaluate at the upper limit:

Plug in x=3 .

$\frac {3(3)^5}{5}+\frac {7(3)^2}{2}+3(3)=\frac {3^6}{5}+\frac {63}{2}+9=186.3$

Step 3: Evaluate at the lower limit:

Plug in x=1 .

$\frac {3(1)^5}{5}+\frac {7(1)^2}{2}+3(1)=\frac {3}{5}+\frac {7}{2}+3=7.1$

Step 4: Take the valuation at the lower limit and subtract it FROM the upper limit:

$186.3-7.1=179.2=\frac {896}{5}$

The integration of 3x^4+7x+3 is $\frac {896}{5}$

Report an Error

Example Question #175 : Definite Integrals

Evaluate:

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

Possible Answers:

Correct answer:

Explanation:

Step 1: Take the antiderivative of each term:

$2x^3 \rightarrow 2 \cdot \frac {x^4}{4}=\frac {x^4}{2}$

$3x^2=3 \cdot \frac {x^3}{3}=x^3$

$3x\rightarrow 3 \cdot \frac {x^2}{2}=\frac {3x^2}{2}$

Step 2: Put all the antiderivatives in step 1 together based on the signs in the integral...

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

Step 3: Plug in the upper and lower limits:

Upper Limit is , lower limit is .

Plug in x=2 :

$\frac {2^4}{2}+2^3+\frac {3(2)^2}{2}=2^3+2^3+3(2)=8+8+6=22$

Plug in x=0 . Since all terms have , the value will be

Step 4: Subtract the value of the lower limit from the upper limit:

22-0=22

The value of this integral is .

Report an Error

Example Question #187 : Finding Integrals

$\int_{0}^{2}4x^2-xdx$

Possible Answers:

$\frac{22}{3}$

$\frac{31}{3}$

$\frac{26}{3}$

$\frac{25}{3}$

$\frac{29}{3}$

Correct answer:

$\frac{26}{3}$

Explanation:

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

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

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

$(\frac{32}{3}-2)-(0)$

Simplify to get your answer:

$\frac{32}{3}-\frac{6}{3}=\frac{26}{3}$

Report an Error

Example Question #172 : Definite Integrals

$\int_{0}^{2}4\sqrt{x}dx$

Possible Answers:

7.5499

7.5425

7.5431

6.5425

7.5295

Correct answer:

7.5425

Explanation:

First, take the 4 outside of the integral sign and rewrite the radical as a fractional exponent. It's easier to visualize that when integrating:

$4\int x^{\frac{1}{2}}dx$

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

$\frac{x^{\frac{3}{2}}}{\frac{3}{2}}$

Simplify and multiply by the 4 that you took out:

$4(\frac{2}{3})x^{\frac{3}{2}}=\frac{8}{3}x^{\frac{3}{2}}$

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

$\frac{8}{3}2^{\frac{3}{2}}-\frac{8}{3}0^{\frac{3}{2}}=7.5425$

Report an Error

Example Question #172 : Definite Integrals

$\int_{1}^{2}3x^2+9dx$

Possible Answers:

Correct answer:

Explanation:

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

$\frac{3x^3}{3}+9x=x^3+9x$

Now, evaluate at 2 and then 1. Subtract the results:
(8+18)-(1+9)=26-10=16

Report an Error

Example Question #174 : Definite Integrals

$\int_{1}^{4}x^2+5x+4dx$

Possible Answers:

$\frac{141}{2}$

$\frac{149}{2}$

$\frac{142}{2}$

$\frac{101}{2}$

$\frac{141}{3}$

Correct answer:

$\frac{141}{2}$

Explanation:

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

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

Now, evaluate at 4 and then 1. Subtract the results:

$(\frac{64}{3}+40+16)-(\frac{1}{3}+\frac{5}{2}+4)$

Simplify to get your answer:

$21+56-4-\frac{5}{2}=\frac{141}{2}$

Report an Error

Example Question #175 : Definite Integrals

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

Possible Answers:

$\frac{22}{3}$

$\frac{50}{3}$

$\frac{55}{3}$

$\frac{20}{3}$

$\frac{47}{3}$

Correct answer:

$\frac{50}{3}$

Explanation:

First, integrate. Remember to raise the exponent by 1 and also put that result on the denominator:
$\frac{x^3}{3}-x$

Now evaluate at 4 and then 2. Subtract the results:
$(\frac{64}{3}-4)-(\frac{8}{3}-2)$

Simplify to get your answer:

$\frac{56}{2}-2=\frac{50}{3}$

Report an Error

View Calculus 2 Tutors

Jeremy
Certified Tutor

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

View Calculus 2 Tutors

Mohammed
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Electrical Engineering. University of Maryland-College Park, Master...

View Calculus 2 Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

All Calculus 2 Resources

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

Popular Subjects

French Tutors in Los Angeles, MCAT Tutors in Boston, Calculus Tutors in Houston, Algebra Tutors in San Francisco-Bay Area, Math Tutors in Seattle, MCAT Tutors in Chicago, SSAT Tutors in Phoenix, MCAT Tutors in Seattle, GMAT Tutors in New York City, SSAT Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in Houston, GMAT Courses & Classes in Miami, SSAT Courses & Classes in Chicago, LSAT Courses & Classes in Phoenix, MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in Houston, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Atlanta, LSAT Test Prep in Chicago, MCAT Test Prep in San Diego, GMAT Test Prep in Houston, GRE Test Prep in New York City, LSAT Test Prep in San Diego, SSAT Test Prep in Seattle, LSAT Test Prep in Boston, SAT Test Prep in Houston, GRE Test Prep in Dallas Fort Worth

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 : Definite Integrals

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #184 : Finding Integrals

Example Question #171 : Definite Integrals

Example Question #186 : Finding Integrals

Example Question #174 : Definite Integrals

Example Question #175 : Definite Integrals

Example Question #187 : Finding Integrals

Example Question #172 : Definite Integrals

Example Question #172 : Definite Integrals

Example Question #174 : Definite Integrals

Example Question #175 : Definite Integrals

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: