We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 … 11 12 13 14 15 16 17 18 19 Next →

Example Question #181 : Integral Expressions

Solve the following integral, where a and b are constants:

$\int abe^{b^2x}dx$

Possible Answers:

$\frac{2ae^{b^2x}}{b}+C$

$\frac{1}{2}ae^{b^2x}+C$

$\frac{ae^{b^2x}}{b}+C$

$ae^{b^2x}+C$

Correct answer:

$\frac{ae^{b^2x}}{b}+C$

Explanation:

Keeping in mind that a and b are only constants, the integral is equal to

$\int abe^{b^2x}dx=\frac{abe^{b^2x}}{b^2}+C=\frac{ae^{b^2x}}{b}+C$

and was found using the following rule:

$\int e^{ax}dx=\frac{e^{ax}}{a}+C$

Report an Error

Example Question #182 : How To Find Integral Expressions

Evaluate the following integral:

$\int xy\cos(x^2y)dx$

Possible Answers:

$\sin(x^2y)+C$

$\frac{1}{2}\sin(x^2y)+C$

$-\frac{1}{2}\sin(x^2y)+C$

$\frac{1}{2}\sin(x^2y)+\frac{x^2y}{2}+C$

Correct answer:

$\frac{1}{2}\sin(x^2y)+C$

Explanation:

To evaluate the integral, we must make the following substitution:

u=x^2y , du=2xydx

The derivative was found using the following rule:

$\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

Rewrite the integral in terms of u and integrate:

$\frac{1}{2}\int \cos(u)du=\frac{1}{2}\sin(u)+C$

The integral was found using the following rule:

$\int \cos(x)dx=\sin(x)+C$

Finally, replace u with our original term:

$\frac{1}{2}\sin(x^2y)+C$ .

Report an Error

Example Question #183 : How To Find Integral Expressions

In circuits with a resistor, the equation for voltage drop is given by:

$\frac{d}{dx}V =\frac{d}{dt}Q*R$ , where is voltage, is charge, and is resistance.

Write the equation as an integral expression for .

Possible Answers:

$Q=\int {\frac{d}{dx}V}R dt$

$Q=\int VR dt$

$Q=\int \frac{V}{R} dt$

$Q=\int \frac{\frac{d}{dx}V}{R} dt$

Correct answer:

$Q=\int \frac{\frac{d}{dx}V}{R} dt$

Explanation:

Although this may seem really difficult, we only need to solve for .

$\frac{d}{dx}V =\frac{d}{dt}Q*R$

$\frac{d}{dt}Q=\frac{\frac{\mathrm{d} }{\mathrm{d} x}V}{R}$

To solve for , integrate both sides:

$Q=\int \frac{\frac{d}{dx}V}{R} dt$

Report an Error

Example Question #182 : Integral Expressions

$\int_{0}^{2}2x^2-5x+1 dx$

Possible Answers:

$\frac{8}{3}$

$-\frac{11}{3}$

$-\frac{5}{3}$

$-\frac{8}{3}$

Correct answer:

$-\frac{8}{3}$

Explanation:

When integrating, remember to add one to the exponent and then put that result on the denominator: $\frac{2x^3}{3}-\frac{5x^2}{2}+x$ . Now evaluate at 2, and then 0. Then subtract the two results. $(\frac{16}{3}-10+2)-0=-\frac{8}{3}$ .

Report an Error

Example Question #185 : How To Find Integral Expressions

$\int \frac{24x^3-2x^2+4x}{4x}dx$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The first step here is to chop this up into three separate terms and then simplify since we have only one denominator: $\int 6x^2-\frac{1}{2}x+1dx$ . Then, integrate each term, remembering to add one to the exponent and then put that result on the denominator: $6(\frac{x^3}{3})-\frac{1}{2}(\frac{x^2}{2})+x$ . Simplify to get your answer: $2x^3-\frac{x^2}{4}+x+C$ . Remember to add C because it is an indefinite integral.

Report an Error

Example Question #186 : How To Find Integral Expressions

$\int \frac{9+x}{x}dx$

Possible Answers:

$9ln\left | x \right |-x+C$

$ln\left | x \right |+x+C$

$\frac{1}{9}ln\left | x \right |+x+C$

$9ln\left | x \right |+x+C$

Correct answer:

$9ln\left | x \right |+x+C$

Explanation:

First, chop this expression up into two terms: $\int \frac{9}{x}+1dx$ . Then, integrate each term, remembering that when there is a single x on a denominator, the integral is $ln\left | x \right |$ . Therefore, the integration is: $9ln\left | x \right |+x+C$ . Remember to add C because it is an indefinite integral.

Report an Error

Example Question #183 : Integral Expressions

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

Possible Answers:

108

Correct answer:

Explanation:

First, integrate each term separately. Remember, when integrating, raise the exponent by one and then also put that result on the denominator: $2(\frac{x^4}{4})-3(\frac{x^3}{3})+\frac{x^2}{2}$ . Then evaluate at 3 and then 0. Subtract two results to get: $(\frac{81}{2}-27+\frac{9}{2})-0=18$ .

Report an Error

Example Question #188 : How To Find Integral Expressions

$\int \sqrt{x}dx$

Possible Answers:

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

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

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

$\frac{2}{3}$

Correct answer:

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

Explanation:

To integrate this expression, I would first rewrite it to be $\int x^{\frac{1}{2}}dx$ . Then, add one to the exponent and then put that result on the denominator: $\frac{x^{\frac{3}{2}}}{\frac{3}{2}}$ . Then, simplify to get your answer of $\frac{2}{3}x^{\frac{3}{2}}+C$ . Remember to add C because it is an indefinite integral.

Report an Error

← Previous 1 2 … 11 12 13 14 15 16 17 18 19 Next →

View Calculus Tutors

Anirudh
Certified Tutor

University of Windsor, Master's/Graduate, Electrical and Computer.

View Calculus Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

View Calculus Tutors

Mahan
Certified Tutor

The University of Texas at Austin, Bachelor of Science, Chemical Engineering. The University of Texas at Austin, Bachelor of ...

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Philadelphia, Math Tutors in Phoenix, Biology Tutors in New York City, Reading Tutors in Houston, MCAT Tutors in Washington DC, GRE Tutors in San Francisco-Bay Area, LSAT Tutors in San Francisco-Bay Area, Chemistry Tutors in Phoenix, SSAT Tutors in Houston, Statistics Tutors in New York City

Popular Courses & Classes

SAT Courses & Classes in Los Angeles, GRE Courses & Classes in Atlanta, SAT Courses & Classes in San Diego, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle, ISEE Courses & Classes in Phoenix, MCAT Courses & Classes in Denver, SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Dallas Fort Worth, SAT Test Prep in Denver, SSAT Test Prep in Philadelphia, ISEE Test Prep in Seattle, SSAT Test Prep in Chicago, MCAT Test Prep in Philadelphia, ACT Test Prep in Washington DC, SSAT Test Prep in Phoenix, GMAT Test Prep in Denver

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 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #181 : Integral Expressions

Example Question #182 : How To Find Integral Expressions

Example Question #183 : How To Find Integral Expressions

Example Question #182 : Integral Expressions

Example Question #185 : How To Find Integral Expressions

Example Question #186 : How To Find Integral Expressions

Example Question #183 : Integral Expressions

Example Question #188 : How To Find Integral Expressions

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: