Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Evaluate the integral. $ \displaystyle \int t …

06:12

Question

Answered step-by-step

Problem 5 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \sin^5 (2t) \cos^2 (2t) dt $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Related Topics

Integration Techniques

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

03:48

Evaluate the integral.

…

06:12

Evaluate the integral.

…

03:12

Evaluate the integral.

…

07:11

Evaluate the integral.
…

04:26

Evaluate the integral.

…

03:42

Evaluate the integral. 5/2…

03:10

Evaluate the integral.
…

00:35

Evaluate the indefinite in…

04:37

Evaluate the integral.

…

00:35

Evaluate the indefinite in…

06:27

Evaluate the integral.

…

04:33

Evaluate the integral.

…

10:46

Evaluate the integral.

…

03:06

Evaluate the integral.

…

02:12

Evaluate the integral.
…

Watch More Solved Questions in Chapter 7

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70

Video Transcript

This problem is from Chapter seven section to Problem number five in the book Capitalists Early Transcendental Sze eighth Edition by James Story Here we have ah, indefinite Integral science of the fifth power of two t co sign squared of two tea. So here, since the power of sign is odd, the first thing we do is rewrite this by pulling out a factor of signs to have signed in the fourth Coastline Square. And let's put that extra factor of sign over here at the end. Chris, observe here in the inner grand that the science of the fourth power. So it's going to decide and rewrite this so we can rewrite sign square science of the four power as Science Square Square. Then we could apply, uh, put that in identity to rewrite sine squared is one minus coastlines where, and we have to square this entire expression and finally weaken. Evaluate this latest expression two co sign squared to team plus coastlines in the fourth power two teams, so replacing science of the forth. With this newest expression, we have the integral one. Minus two co signed square plus coast under the fourth Power Time's Cose identity to co sign squared to tease and sign off duty. So here it looks like we can apply u substitution here we should take you two be co sign opportunity, which implies to you is negative, too. Sign two t d t. That's using the chain rule and here because we don't have a negative to in front of the sign and the original under grand, we should make up for this, but by multiplying by a negative one half in front of the to you to give us exactly what we want. Sign two tea Titi Just as appears an immigrant. So now let's rewrite this integral using our U substitution. So first, let's pull off this negative on half outside the integral level one minus to use Claire. Plus, you know, the fourth then co sign squared is just use Claire and then to you. So now let's just leave this negative one half outside for now. And what's the stripy tissue squared inside the apprentices. So we have a use clear minus to you to the fourth power. Plus, you know the city's power to you to evaluate the center girl. We should supply the power rule three times. So we have you to the third power over three minus to you to the fifth over five. Plus, you're the seven over seven, plus our constancy of integration. So here we have two steps left will replace you with co sign of two tea, and we could multiply by this negative one have so we get a negative cool sign. Cube's Tootie over six. Here we have a plus coastline to the fifth hour over five. Those two's cancel. Now we have a minus co sign to the seventh hour, all divided by fourteen and closer constancy, and that's our answer.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
83
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
53
Hosted by: Alonso M
See More

Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Michael Jacobsen

Idaho State University

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
Recommended Videos

03:48

Evaluate the integral. $ \displaystyle \int \sin^5 (2t) \cos^2 (2t) dt $

06:12

Evaluate the integral. $ \displaystyle \int t \cos^5 (t^2) dt $

03:12

Evaluate the integral. $ \displaystyle \int \sin^5 t \cos^4 t\ dt $

07:11

Evaluate the integral. $$\int \sin ^{5}(2 t) \cos ^{2}(2 t) d t$$

04:26

Evaluate the integral. $ \displaystyle \int_0^{2 \pi} t^2 \sin 2t dt $

03:42

Evaluate the integral. 5/2 cos(5t) cos(10t) dt

03:10

Evaluate the integral. $$\int t \cos ^{5}\left(t^{2}\right) d t$$

00:35

Evaluate the indefinite integral. $ \displaystyle \int \cos (1 + 5t) \, dt $

04:37

Evaluate the integral. $ \displaystyle \int_0^{\frac{\pi}{2}} \cos 5t \cos 1…

00:35

Evaluate the indefinite integral. $ \displaystyle \int 5^t \sin(5^t) \, dt $

06:27

Evaluate the integral. $ \displaystyle \int_0^\pi \cos^4 (2t) dt $

04:33

Evaluate the integral. $ \displaystyle \int t \sin^2 t dt $

10:46

Evaluate the integral. $ \displaystyle \int_0^\pi \sin^2 t \cos^4 t dt $

03:06

Evaluate the integral. $ \displaystyle \int \frac{\sin^2 \left(\frac{1}{t} \…

02:12

Evaluate the integral. $$ \int \cos ^{3}(t / 2) \sin ^{2}(t / 2) d t $$
Additional Mathematics Questions

05:39

The metabolic rate of a person who has just eaten a meal tends to go up and …

02:20

Writing Write a short paragraph explaining the differences between the recta…

02:15

Write an equation. Then solve the equation without graphing.
Protactinium…

01:47

Use a graphing device to draw the curve represented
by the parametric equ…

01:18

If $A$ is singular, what can you say about the product $A$ adj $A ?$

01:18

If $A$ is singular, what can you say about the product $A$ adj $A ?$

04:30

Show that if $A$ is nonsingular, then adj $A$ is nonsingular and
$$
(\…

02:11

Let $x$ and $y$ be linearly independent vectors in $\mathbb{R}^{2}$. If $\|x…

02:52

Find the distance from the point $(2,1,-2)$ to the plane
$$6(x-1)+2(y-3)+…

06:31

Let $C$ be a nonsymmetric $n \times n$ matrix. For each of the following, de…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started