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Problem

Verify Formula 53 in the Table of Integrals (a) b…

04:17

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Problem 34 Hard Difficulty

Find the volume of the solid obtained when the region under the curve $ y = \arcsin x $, $ x \ge 0 $, is rotated about the y-axis.


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 6

Integration Using Tables and Computer Algebra Systems

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.

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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

Video Transcript

Okay, This question Once a stir of all of the area underneath Weikel sine inverse X, where X is greater than zero around the y axis. So, with all volume of revolution questions, let's draw to see what we're dealing with. So Arc Sine has a domain from negative one No one. So if we're considering the positive side, we end at one here. And then if we graph park sign of X, it looks something like this, but we're evolving this area around the Y axis. So what we can do is convert this to a function of X and consider this area right here. And remember this Y value is pirate, too, because arc sine of one is pirates. So to convert to a function of acts, we could just see that sign of why equals X. So that becomes are integral. So are equals. Sign Why? So that means air volume is pi times the integral from zero to pi over too of sign of why squared d y and no, that's an integral that we can look up. Or at this point, you may have it memorized. So the integral of sine squared is 1/2 why minus 1/4 sign of two. Why? From 0 to 2. Pi Sorry, zero pi over too. And this becomes pi Times pi over two divided by two minus Well signed pie is zero minus 1/2 time. Zero minus 1/4 time. Zero. So this is just equal to pi times pi over two divided by two, which is equal to high times over for or pi squared over for so that's our final answer.

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Calculus: Early Transcendentals

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Related Topics

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Top Calculus 2 / BC Educators
Grace He

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Anna Marie Vagnozzi

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Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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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