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 #111 : Definite Integrals

Evaluate.

$\int_{1}^{2} e^{43x -30} \ dx$

Possible Answers:

$\frac{e^{56}}{43}-\frac{e^{13}}{43}$

-0.75

Answer not listed.

5.21

6.54

Correct answer:

$\frac{e^{56}}{43}-\frac{e^{13}}{43}$

Explanation:

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

In this case, $f(x) = e^{43x -30}$ .

The antiderivative is $F(x) =\frac{ e^{43x -30}}{43}$ .

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

$\int_{1}^{2} e^{43x -30} \ dx = \left ( \frac{ e^{43x -30}}{43} \right )_{1}^{2}$

$=\frac{ e^{43(2) -30}}{43} - \left ( \frac{ e^{43(1) -30}}{43} \right )$

$=\frac{e^{56}}{43}-\frac{e^{13}}{43}$

Report an Error

Example Question #112 : Definite Integrals

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

Possible Answers:

Correct answer:

Explanation:

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

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

Then, evaluate first at 5 and then at 2. Subtract those two results:

$(\frac{125}{3}+50-5)-(\frac{8}{3}+8-2)=\frac{117}{3}+39=78$ .

Thus, your answer is 78.

Report an Error

Example Question #113 : Definite Integrals

$\int_{1}^{3}\frac{5+3x}{x}dx$

Possible Answers:

11.4978

11.4931

11.5731

12.4931

11.4631

Correct answer:

11.4931

Explanation:

First, chop up the fraction into two separate terms:

$\int_{1}^{3}\frac{5}{x}+3dx$

Now, integrate. Remember that when there is a single x on the denominator, the integral is ln of that term.

$5ln\left | x \right |+3x$

Evaluate at 3 and then at 1. Subtract the results:

(5ln3+9)-(5ln1+3)=11.4931 .

Report an Error

Example Question #114 : Definite Integrals

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

Possible Answers:

$\frac{112}{5}$

$\frac{112}{3}$

$\frac{113}{3}$

$\frac{101}{3}$

$\frac{92}{3}$

Correct answer:

$\frac{112}{3}$

Explanation:

First, use FOIL to multiply the binomials before integrating:

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

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

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

Evaluate at 4 and then 2. Subtract the results:

$(\frac{128}{3}+\frac{16}{2}-12)-(\frac{16}{3}+\frac{4}{2}-6)=\frac{112}{3}$

Report an Error

Example Question #115 : Definite Integrals

Evaluate.

$\int_{1}^{2}12x-9 dx$

Possible Answers:

Answer not listed.

Correct answer:

Explanation:

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

In this case, f(x) = 12x-9 .

The antiderivative is F(x) = 6x^2-9x .

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

$\int_{1}^{2}12x-9 dx = \left ( 6x^2-9x \right )_{1}^{2}$

$= 6(2)^2-9(2)- \left ( 6(1)^2-9(1) \right )$

= 8

Report an Error

Example Question #116 : Definite Integrals

Evaluate.

$\int_{1}^{2} 13 \ dx$

Possible Answers:

Answer not listed

Correct answer:

Answer not listed

Explanation:

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

In this case, f(x) = 13 .

The antiderivative is F(x) = 13x .

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

$\int_{1}^{2} 13 \ dx = \left ( 13x \right )_{1}^{2}$

$= 13(2) - \left ( 13(1) \right )$

= 13

Report an Error

Example Question #117 : Definite Integrals

Evaluate.

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

Possible Answers:

0.46

1.08

2.11

Answer not listed.

-1.62

Correct answer:

1.08

Explanation:

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

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

The antiderivative is $F(x) = -3 \ln(3-x) - x$ .

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

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

$= -3 \ln(3-2) - 2 - \left ( -3 \ln(3-1) - 1 \right )$

= 1.08

Report an Error

Example Question #118 : Definite Integrals

Evaluate.

$\int_{3}^{4}e^{2x-5} \ dx$

Possible Answers:

5.8

9.3

8.7

2.4

4.1

Correct answer:

8.7

Explanation:

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

In this case, $f(x) = e^{2x-5}$ .

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

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

$\int_{3}^{4}e^{2x-5} \ dx= \left ( \frac{e^{2x-5} }{2} \right )_{3}^{4}$

$=\frac{e^{2(4)-5} }{2} - \left ( \frac{e^{2(3)-5} }{2} \right )$

= 8.7

Report an Error

Example Question #119 : Definite Integrals

Evaluate.

$\int_{1}^{2} \sin (5x-3) \ dx$

Possible Answers:

1.023

2.421

0.935

0.001

-0.545

Correct answer:

0.001

Explanation:

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

In this case, $f(x) = \sin (5x-3)$ .

The antiderivative is $F(x) = -\frac{ \cos(5x-3) }{5}$ .

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

$\int_{1}^{2} \sin (5x-3) \ dx = \left ( -\frac{ \cos(5x-3) }{5} \right )_{1}^{2}$

$=-\frac{ \cos(5(2)-3) }{5} - \left ( -\frac{ \cos(5(1)-3) }{5} \right )$

= 0.001

Report an Error

Example Question #120 : Definite Integrals

Evaluate.

$\int_{0}^{1}\sec^2(3x) \ dx$

Possible Answers:

Answer not listed.

1.09

-0.35

1.24

-0.05

Correct answer:

-0.05

Explanation:

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

In this case, $f(x) = \sec^2(3x)$ .

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

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

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

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

= -0.05

Report an Error

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...

View Calculus 2 Tutors

Robert
Certified Tutor

University of Guelph, Bachelor, Biochemistry.

All Calculus 2 Resources

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

Popular Subjects

Calculus Tutors in San Francisco-Bay Area, LSAT Tutors in Miami, SSAT Tutors in Miami, Algebra Tutors in Denver, Physics Tutors in Chicago, English Tutors in Dallas Fort Worth, LSAT Tutors in Washington DC, Calculus Tutors in Atlanta, ISEE Tutors in Boston, Calculus Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Seattle, SAT Courses & Classes in Denver, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Denver, ACT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in New York City, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Atlanta

Popular Test Prep

SAT Test Prep in Philadelphia, MCAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Boston, SAT Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, ISEE Test Prep in Denver, MCAT Test Prep in Houston, GRE Test Prep in Washington DC, SAT Test Prep in Chicago

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 #111 : Definite Integrals

Example Question #112 : Definite Integrals

Example Question #113 : Definite Integrals

Example Question #114 : Definite Integrals

Example Question #115 : Definite Integrals

Example Question #116 : Definite Integrals

Example Question #117 : Definite Integrals

Example Question #118 : Definite Integrals

Example Question #119 : Definite Integrals

Example Question #120 : Definite Integrals

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: