We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : 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 #15 : Integral Applications

A ball has a velocity defined by v(t)=3t-4 , where we express in seconds. What distance does it travel between $0\leq t\leq 3$ in meters?

Possible Answers:

$\frac{5}{2}m$

$\frac{5}{3}m$

$\frac{2}{3}m$

None of the above

$\frac{3}{2}m$

Correct answer:

$\frac{3}{2}m$

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since

v(t)=3t-4 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{3}(3t-4)dt$

$=[\frac{3}{2}t^{2}-4t]_{0}^{3}$

$=[\frac{3}{2}(3)^{2}-4(3)]-[\frac{3}{2}(0)^{2}-4(0)]$

$=\frac{27}{2}-12$

$=\frac{27}{2}-\frac{24}{2}$

$=\frac{3}{2}$

Report an Error

Example Question #11 : Applications In Physics

A subway has a velocity defined by v(t)=11t+9 , where we express in seconds. What distance does it travel between $0\leq t\leq 4$ in meters?

Possible Answers:

122m

130m

124m

126m

128m

Correct answer:

124m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since

v(t)=11t+9 ,

we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{4}(11t+9)dt$

$=[\frac{11}{2}t^{2}+9t]_{0}^{4}\textrm{}$

$=\frac{176}{2}+36$

=88+36

=124

Report an Error

Example Question #17 : Integral Applications

A train goes a certain distance between $0\leq t \leq 2$ (where is time in seconds). If we know that the train's velocity is defined as v(t)=12t+15 , what is the distance it travelled (in meters)?

Possible Answers:

56m

50m

45m

46m

54m

Correct answer:

54m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=12t+15 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{2}(12t+15)dt$

$=[6t^{2}+15t]_{0}^{2}\textrm{}$

$=[6(2)^{2}+15(2)]-[6(0)^{2}+15(0)]$

=[24+30]

=54

Report an Error

Example Question #18 : Integral Applications

A car goes a certain distance between $0\leq t \leq 3$ (where is time in seconds). If we know that the car's velocity is defined as v(t)=14t-2 , what is the distance it travelled (in meters)?

Possible Answers:

55m

59m

58m

56m

57m

Correct answer:

57m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=14t-2 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{3}(14t-2)dt$

$=[7t^{2}-2t]_{0}^{3}\textrm{}$

$=[7(3)^{2}-2(3)]-[7(0)^{2}-2(0)]$

=[63-6]

=57

Report an Error

Example Question #11 : Integral Applications

A plane goes a certain distance between $2\leq t \leq 5$ (where is time in seconds). If we know that the plane's velocity is defined as v(t)=6t-2 , what is the distance it travelled (in meters)?

Possible Answers:

60m

61m

57m

58m

59m

Correct answer:

57m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=6t-2 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{2}^{5}(6t-2)dt$

$=[3t^{2}-2t]_{2}^{5}\textrm{}$

$=[3(5)^{2}-2(5)]-[3(2)^{2}-2(2)]$

=75-10-12+4

=57

Report an Error

Example Question #21 : Applications In Physics

The velocity of a ship is defined as $v(t)=\frac{1}{2}t+9$ (where time is measured in seconds). What distance (in meters) does the ship travel between seconds and seconds?

Possible Answers:

19m

22m

21m

18m

20m

Correct answer:

19m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since $v(t)=\frac{1}{2}t+9$ , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{2}(\frac{1}{2}t+9)dt$

$=[\frac{1}{4}t^{2}+9t]_{0}^2{}\textrm{}$

Since the definite integral at is , we get:

$=\frac{1}{4}(2)^{2}+9(2)$

=1+18

=19

Report an Error

Example Question #22 : Applications In Physics

The velocity of a car is defined as v(t)=5t+6 (where time is measured in seconds). What distance (in meters) does the car travel between seconds and seconds?

Possible Answers:

$\frac{79}{2}m$

$\frac{80}{2}m$

$\frac{83}{2}m$

$\frac{82}{2}m$

$\frac{81}{2}m$

Correct answer:

$\frac{81}{2}m$

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=5t+6 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{3}(5t+6)dt$

$=[\frac{5}{2}t^{2}+6t]_{0}^{3}\textrm{}$

Since the definite integral at is , we get:

$=\frac{5}{2}(3)^{2}+6(3)$

$=\frac{45}{2}+18$

$=\frac{45}{2}+\frac{36}{2}$

$=\frac{81}{2}$

Report an Error

Example Question #191 : Integrals

The velocity of a rocket is defined as v(t)=12t+7 (where time is measured in seconds). What distance (in meters) does the rocket travel between second and seconds?

Possible Answers:

172m

173m

170m

174m

171m

Correct answer:

172m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=12t+7 , we can use the Power Rule for Integrals

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{1}^{5}(12t+7)dt$

$=[6t^{2}+7t]_{1}^{5}\textrm{}$

$=[6(5)^{2}+7(5)]-[6(1)^{2}+7(1)]$

=[185]-[13]

=172

Report an Error

Example Question #24 : Applications In Physics

A dog travels a certain distance between seconds and seconds. If we define its velocity as v(t)=6t-5 , what is that distance in meters?

Possible Answers:

Correct answer:

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=6t-5 , we can use the Power Rule for Integrals

$\int t^{n}dt=\frac{t^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{2}(6t-5)dt$

$=[3t^{2}-5t]_{0}^{2}$

$=[3(2)^{2}-5(2)]-[3(0)^{2}-5(0)]$

=[12-10]

Report an Error

Example Question #25 : Applications In Physics

A skateboarder travels a certain distance between seconds and seconds. If we define her velocity as v(t)=2t+1 , what is her distance in meters?

Possible Answers:

20m

25m

30m

10m

15m

Correct answer:

20m

Explanation:

We define velocity as the derivative of distance, or v(t)=d'(t) .

Thus, in order to find the distance traveled when given the velocity, we'll need to take the definite integral of the velocity function over a specified time period, or $\int_{a}^{b}v(t)dt$ .

Since v(t)=2t+1 , we can use the Power Rule for Integrals

$\int t^{n}dt=\frac{t^{n+1}}{n+1}$ for all $n\neq0$ ,

to find:

$\int_{0}^{4}(2t+1)dt$

$=[t^{2}+t]_{0}^{4}$

$=[4^{2}+4]-[(0)^{2}+(0)]$

=16+4

=20

Report an Error

View Calculus 2 Tutors

Vincent
Certified Tutor

Bridgewater State University, Bachelor of Science, Computer and Information Sciences, General.

View Calculus 2 Tutors

Oluwatosin
Certified Tutor

Illinois Institute of Technology, Bachelor of Engineering, Computer Engineering, General.

View Calculus 2 Tutors

Carlos
Certified Tutor

CUNY City College, Bachelor of Engineering, Electrical Engineering.

All Calculus 2 Resources

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

Popular Subjects

English Tutors in Los Angeles, SAT Tutors in Houston, Algebra Tutors in Denver, English Tutors in Washington DC, Spanish Tutors in Philadelphia, Computer Science Tutors in Boston, Physics Tutors in New York City, Biology Tutors in Houston, Statistics Tutors in Chicago, English Tutors in Houston

Popular Courses & Classes

GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston, SSAT Courses & Classes in Washington DC, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Boston, MCAT Courses & Classes in Miami, Spanish Courses & Classes in San Diego, MCAT Courses & Classes in Denver, SAT Courses & Classes in Miami, ACT Courses & Classes in Atlanta

Popular Test Prep

MCAT Test Prep in Phoenix, LSAT Test Prep in Miami, ISEE Test Prep in New York City, GMAT Test Prep in Philadelphia, ACT Test Prep in Los Angeles, ISEE Test Prep in Denver, ACT Test Prep in Philadelphia, MCAT Test Prep in New York City, SSAT Test Prep in Phoenix, MCAT Test Prep in Seattle

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 : Integrals

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #15 : Integral Applications

Example Question #11 : Applications In Physics

Example Question #17 : Integral Applications

Example Question #18 : Integral Applications

Example Question #11 : Integral Applications

Example Question #21 : Applications In Physics

Example Question #22 : Applications In Physics

Example Question #191 : Integrals

Example Question #24 : Applications In Physics

Example Question #25 : Applications In Physics

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: