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

Example Question #2221 : Calculus

Evaluate the following integral:

$\int( e^{2x}+\cos(2x))dx$

Possible Answers:

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

$(e^{2x}-\sin(2x))+C$

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

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

Correct answer:

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

Explanation:

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

u=2x, du=2dx

Now, rewrite the integral and integrate:

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

The integration was performed using the following rules:

$\int e^xdx=e^x+C, \int \cos(x)dx=\sin(x)=C$

Finally, replace u with our original x term:

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

Report an Error

Example Question #141 : How To Find Integral Expressions

Evaluate the following integral:

$\int (x^2+7x+\sin(x))dx$

Possible Answers:

$\frac{x^3}{3}+{7x^2}-\cos(x)+C$

$x^3+\frac{7x^2}{2}-\cos(x)+C$

$\frac{x^3}{3}+\frac{7x^2}{2}-\cos(x)+C$

$\frac{x^3}{3}+\frac{7x^2}{2}+\cos(x)+C$

Correct answer:

$\frac{x^3}{3}+\frac{7x^2}{2}-\cos(x)+C$

Explanation:

The integral is equal to

$\frac{x^3}{3}+\frac{7x^2}{2}-\cos(x)+C$

and was evaluated using the following rules:

$\int x^ndx=\frac{x^{n+1}}{n+1}+C$ , $\int \sin(x)dx=-\cos(x)+C$

Report an Error

Example Question #142 : How To Find Integral Expressions

Integral

If f(x) is even,

$\int_{-a}^{a}f(x)dx= 2\int_{0}^{a}f(x)dx$

Possible Answers:

The statement is true

It is called differentiating odd functions

The statement is false

It is called differentiating even functions

None of the above

Correct answer:

The statement is true

Explanation:

According to the integration of even function rule,

$\int_{-a}^{a}f(x)dx= 2\int_{0}^{a}f(x)dx$

Report an Error

Example Question #144 : Equations

Write the integral expression for the area under the following curve from x=1 to x=6 .

f(x)=4x^2-3x+1

Possible Answers:

$\int_{1}^{6}(4x^2-3x+1)dx$

$\int_{1}^{6}(8x-3)dx$

$\int_{6}^{1}(4x^2-3x+1)dx$

$\int_{1}^{6}4x^2-3x+1$

Correct answer:

$\int_{1}^{6}(4x^2-3x+1)dx$

Explanation:

To write the integral expression, simply set the bounds given with the smaller on the bottom and don't forget the . Thus,

$\int_{1}^{6}(4x^2-3x+1)dx$

Report an Error

Example Question #143 : How To Find Integral Expressions

Find the integral of the following equation from to {-2} .

f(x)=x^2-5x-100

Possible Answers:

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

$\int_{-2}^{2}(x^2-5x-100)dx$

$\int_{2}^{-2}(x^2-5x-100)dx$

$\int_{2}^{-2}x^2-5x-100$

Correct answer:

$\int_{2}^{-2}(x^2-5x-100)dx$

Explanation:

To solve, simply plug in your bounds and equation. Make sure to note how the order of bounds was said in the problem. Thus,

$\int_{2}^{-2}(x^2-5x-100)dx$

Report an Error

Example Question #144 : Integral Expressions

Evaluate the following integral:

$\int 3\sin(x)e^{\cos(x)}dx$

Possible Answers:

$3e^{\cos(x)}+C$

$-3e^{\cos(x)}+C$

$-3e^{-\cos(x)}+C$

$-3e^{\sin(x)}+C$

Correct answer:

$-3e^{\cos(x)}+C$

Explanation:

To evaluate the integral, we must perform the following subsitution:

$u=\cos(x), du=-\sin(x)dx$

The derivative was found using the following rule:

$\frac{\mathrm{d} }{\mathrm{d} x} \cos(x)=-\sin(x)$

Now, rewrite the integral and integrate:

$-3\int e^udu=-3e^u+C$

The integral was found using the following rule:

$\int e^udu=e^u+C$

Finally, replace u with the original term:

$-3e^{\cos(x)}+C$

Report an Error

Example Question #144 : How To Find Integral Expressions

Evaluate: $\int_{0}^{3} 6x^2 + 5x - 1 \,\mathrm{d}x$

Possible Answers:

73.5

$\frac{37}{3}$

Correct answer:

73.5

Explanation:

To find the integral, first find the antiderivative, then evaluate at the limits of integration to find the definite integral.

Here, the antiderivative is $\small \small F(x) = 2x^3 + \frac{5}{2}x^2 - x+C$ .

$\small F(3) - F(1) = 73.5 - 0 = 73.5$

Report an Error

Example Question #147 : Equations

Integrate:

$\int 3x^2+4x-1 dx$

Possible Answers:

x^3+x^2-x+C

2x^3+2x^2-1+C

x^3+2x^2+C

x^3+2x^2-1

x^3+2x^2-x+C

Correct answer:

x^3+2x^2-x+C

Explanation:

When integrating this expression, tackle each term separately. For $3x^{2}$ , leave the out and just integrate the term. Raise the exponent by and then put that result on the denominator: $3(\frac{x^3}{3})$ . Do that for each term. becomes $4(\frac{x^2}{2})$ and becomes . Put those all together and add a "C" at the end because it is an indefinite integral: x^3+2x^2-1+C .

Report an Error

Example Question #146 : Integral Expressions

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

Possible Answers:

$\frac{1}{3}x^3+x^2-x$

x^3+x^2-x+C

$\frac{1}{3}x^3+x^2-x+C$

$\frac{1}{3}x^3+2x+C$

$\frac{1}{3}x^3-2x^2-x+C$

Correct answer:

$\frac{1}{3}x^3+x^2-x+C$

Explanation:

Before integrating this expression, I would chop it up into three separate terms and simplify since there is only one term on the denominator: $\int x^2+2x-1dx$ . Then, integrate each term separately. When you integrate, you raise the exponent by and then put that result on the denominator. Therefore, the resulting expression after integrating is: $\frac{x^3}{3}+\frac{2x^2}{2}-x$ . Simplify and add a "C" at the end (it's an indefinite integral) and the answer is:

$\frac{1}{3}x^3+x^2-x+C$ .

Report an Error

Example Question #147 : Integral Expressions

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

Possible Answers:

$\frac{26}{3}$

$-\frac{26}{3}$

$\frac{1}{26}$

Correct answer:

$\frac{26}{3}$

Explanation:

First, just focus on integrating the expression before evaluating it. When integrating, raise the exponent by one and then put that result on the denominator. Therefore, after integrating, you get: $3(\frac{x^4}{4})-2(\frac{x^3}{3})+x$ . Then, plug in , which yields $\frac{26}{3}$ and then subtract the result of when you plug in .

$\frac{26}{3}-0=\frac{26}{3}$ .

Report an Error

View Calculus Tutors

Shree
Certified Tutor

Tufts University, Bachelor in Arts, Political Science and Government.

View Calculus Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Calculus Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

All Calculus 1 Resources

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

Popular Subjects

LSAT Tutors in Los Angeles, Algebra Tutors in San Diego, Algebra Tutors in Atlanta, Reading Tutors in New York City, English Tutors in Dallas Fort Worth, Biology Tutors in Seattle, Physics Tutors in New York City, GMAT Tutors in Miami, SAT Tutors in Atlanta, Chemistry Tutors in Houston

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Atlanta, LSAT Courses & Classes in Denver, SAT Courses & Classes in Denver, ACT Courses & Classes in Atlanta, LSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Washington DC, GRE Courses & Classes in Denver, ACT Courses & Classes in Los Angeles, ISEE Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Boston, GMAT Test Prep in Miami, ACT Test Prep in Los Angeles, GRE Test Prep in Denver, GRE Test Prep in San Diego, SSAT Test Prep in Seattle, SAT Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, GMAT Test Prep in Houston, GRE Test Prep in Atlanta

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 #2221 : Calculus

Example Question #141 : How To Find Integral Expressions

Example Question #142 : How To Find Integral Expressions

Example Question #144 : Equations

Example Question #143 : How To Find Integral Expressions

Example Question #144 : Integral Expressions

Example Question #144 : How To Find Integral Expressions

Example Question #147 : Equations

Example Question #146 : Integral Expressions

Example Question #147 : Integral Expressions

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: