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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

$V=9 \pi \ln 3-4 \pi$

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Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

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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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Topics

Integration Techniques

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Samuel H.

University of Nottingham

Lectures

Join Bootcamp