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Evaluate the integral. $ \displaystyle \int_0^…

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Problem 28 Hard Difficulty

Evaluate the integral.

$ \displaystyle \int_0^{2 \pi} t^2 \sin 2t dt $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

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Top Calculus 2 / BC Educators
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Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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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.

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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
Problem 71
Problem 72
Problem 73
Problem 74

Video Transcript

The problem is you want No. It is integral Integral from zero to two pie He squired hams Sign Tuti, didn't he? But this problem, we can use my third of the integration by parts The farmer is into girl from a to B You come from a crumb? He x If you go to you come three from hate being minus the integral I'm paid to be you. Prom time Savi yaks Our problem we cannot you is equal to he's squire on Dwi prom Is Nico to sign? Sure. Then you promise Legal to Truchi and we think about you. Negative one half sign thirteen now by this family this integral is he Go to utensil. Lisa, this is negative. One half his squire who signed John T from zero to high minus integral off you prom times We'd This's shoot. I'm selective. One half sign to tea. He from zero to too high. This is the control. The first, the term we're plugging to pie on zero to tea. This's the control. Negative. Well, half times Opie Squire minus. There's a class into girl from there Too high. He hams signed truth here in here now felt fists into girl. We can also use integration. Their parts like you is equal to he. We promise you go to co sign to the and then you prom. It's even want on Vesey Goto Behalf hams sign to tea. So this is the culture. The first two term is negative. Two pi square, then plus you temps. We is one half need cams signed two t from zero to you pie minus into girl of your prom times. Liza, this is half sign to a T E T. From zero to to pie. Now, this is the CO two next to two Pi squire on DH. This term is equal to zero. This is minus one Force sign shoot from their own to Opie. Ondas Under is negative two Pi squire Andi Myers one Force Juan Months Juan. The answer is negative. Too high square.

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Calculus: Early Transcendentals

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Joseph Lentino

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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