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Problem

First make a substitution and then use integratio…

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Problem 39 Hard Difficulty

First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int_{\sqrt{\frac{\pi}{2}}}^{\sqrt{\pi}} \theta^3 \cos (\theta^2) d \theta $


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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

Discussion

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Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

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University of Michigan - Ann Arbor

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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 first maker substitution on DH. Then use integration. My parts Teo Why, I'd have been to grow so faint. Signal is into girl from return of pie over to two Frito Pie. The disco fits Q times consign clear the square. The first I can use use of prostitution. But they go to data squad, then the US is the ax too. Two times you stay there. Now this integral is you called too into girl from high over two to pie. The square is facts on the deep has one half the axe and assign Get square is consign Since this integral is factual into peril from pie or two to pine one half times Max um school sign axe. Now this is Carter would have Here is one half times pi work to pie. Sykes, Jax. Now we can use integration. My pass. So the formula is into girl from a to B you be prime the axe. It's the call to you have sleeve from a B minus in general, from a to B your prime housefly axe. Oh, our problem. We can let you is equal to x and they re prom is recalled to assign Max. Then you prom is equal to one. Read it. Sign acts now this into your office. Hans Newtown Suiza, this is X Hammes Sign. Thanks from hi over to two. Minus into your own. Your prime time squeezes. This is Sign Axe from high work. You too. Hi. I think so too. My half first term. This zero minus pi over two and interior ofthe sign Axe is negative. Kasai Axe, This's class Sign Max from high over to too high. This is one half. I'm selective pie. Over two. They assign highs. Makes you want fine power to zero, which is the answer is half half snaked. Your power too minus one.

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Calculus: Early Transcendentals

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Related Topics

Integration Techniques

Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

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
Recommended Videos

07:46

First make a substitution and then use integration by parts to evaluate the int…

04:48

First make a substitution and then use integration by parts to evaluate the in…

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Use two or more substitutions to find the following integrals. $$\int_{0}^{\pi …

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$33-38$ First make a substitution and then use integration by parts to evaluat…

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Integrate: $\int \frac{\cos \theta}{\sin ^{2} \theta+2 \sin \theta-3} d \theta …

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Use integration by substitution and the Fundamental Theorem to evaluate the def…

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Use the Substitution Rule for Definite Integrals to evaluate each definite inte…

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Integrate each of the functions. $$\int_{\pi / 3}^{\pi / 2} \frac{2 \sin \theta…

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Please Solve, thank you!
Additional Mathematics Questions

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A box contains 5 radio tubes of which 2 are defective.The tubes are tested o…

00:26

Evaluate the following limits. limit x→-1 x^3 + 1x + 1 .
A. 3

01:27

Evaluate (using factors) : 301^2 × 300 - 300^3
A. 180300

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Find the derivative of 99x at x = 100 .

01:27

Find the range of the function f(x) = e^2x + 1 .

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