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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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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:53

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.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

03:07

Use the method of cylindri…

00:59

07:10

10:27

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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