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Problem

Calculate the volume generated by rotating the re…

05:56

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Problem 64 Hard Difficulty

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves about the given axis.

$ y = e^x $ , $ x = 0 $ , $ y = 3 $ ; about the x-axis


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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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Oregon State University

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Lectures

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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 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

problem is youth of my third of cylindrical shells. Tto find the wallet generated by taking the region party the curves but given access You know why? As they got to stacks Excuse equal to zero And why's he can't with three Father the X axis First week Unjust graph. This is the graph. Why would be to ACS accede with zero? And why two three? This is like three So the region is this part. If we take this region about X axis on youth cylindrical shells Mother then we have the got you into Drew from here. This is Juan. This's three. So this is from one three and to pie things. This region is irritated about axe access. So this is a two part. Why has it's why they put it? Walks hikes is they caught your friend? Why, This is too high Line times one Why b y this is too high. Integral from want three. Why, Helen? Why you want now we can use integration. My pars yourself. Listen, integral farmer is integral from a to B you be from yaks. It's the culture You'd have being minus the integral from a to B Your crown, ma'am sleeve yaks. Now we can like you is because you're out. And why, Andre? Promise you could. Why, then you promise people to one over. Why? And we got you Half Ham's Weiss quarter. Now this integral is too high. Hams. Newtown squeezes. This is what half? Why square out and why? From one, two, three minus and to go off from one to three. You prom time species. This is my half. Why do you want this? This country? Oh, hi Times. Plucking three and watch. Why? How's this nine over too. How? In? Three minus zero. Minus one. Force. Why, squire from one to three. This is a culture too high. Mine over to challenge three minus one force. It's nine minus. Juan. This is too high. Nine over. Two times out in three minus two. This's answer

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Top Calculus 2 / BC Educators
Heather Zimmers

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University of Michigan - Ann Arbor

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
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