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Problem

Evaluate the integral. $ \displaystyle \int_2^…

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Problem 8 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int t \sin t \cos t\ dy $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 5

Strategy for Integration

Related Topics

Integration Techniques

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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.

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Watch More Solved Questions in Chapter 7

Problem 1
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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
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Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84

Video Transcript

Let's use integration. My parts for this one. Let's take you to BT So that do you equals DT and then we're left over with Devi equals sign times co sign DT then the You could find this by just integrating. And this in a girl you've seen earlier in the chapter, you could do a use up here or let's use different letter w equal society. And here we'LL get science Where Over too And as usual, when using integration my parts Let's not add the constant C right now. Well, add that in the very end. So here, using the integration by parts you have beauty minus integral video Long has put Are you Indian? So this is our you and Harvey and then minus and a girl. And now we have V again and then do you? So we pull out that to outside the integral in half and then we just have signed square. Now for this you'LL use the half ingle formula If the right is one minus co sign to tea all over too. So let's go ahead and write that. And so combining those twos we get one over four in general one minus cose. Ianto T. Now there's two here. If that's bothering you, you could do another use up here. Let's, um, he's a different different letter here instead of you. Since it's already being used here, you could do another u sub and we should get T Thanks. Word over to still minus. And now we have one over four with the minus, and then that integral of one becomes a T. So that's minus t over. For here. We have a double minus that becomes a plus, and then we have one over four signed t over two plus e. Finally, we got our constant of integration and the last step here isjust combined just a multiply those denominators out. So now we have plus sign to t over eight plus e, and that's our answer.

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Top Calculus 2 / BC Educators
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Idaho State University

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Boston College

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
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