Download presentation

Presentation is loading. Please wait.

Published byEllis Chumbley Modified over 8 years ago

2
Find the volume of y= X^2, y=4 revolved around the x-axis Cross sections are circular washers Thickness of the washer is xsub2-xsub1 Step 1) Find the thickness. (Volume of entire)^2 – (Volume of the “hole”)^2. In this case it is (4)^2-(X^2)^2

3
Step 2) Find the bounds. Because y=4 and y=x^2 intersect at x=-2 and x=2, those are your bounds. Step 3) Plug all the information into the integral It should like this : from x=-2 to x=2 of (4)^2- (X^2)^2 all multiplied by pie The answer should be : 256pie/5

4
Find the volume of y=X^2 between x=0 and x=1 revolved around the x-axis Step 1) For this problem, you must do “top- bottom” to find the “thickness”, so it is ((x^2)-0) Step 2) Next, you must find the bounds. As given in the problem, the bounds are from x=0 to x=1

5
Step 3) Set up the integral from x=0 to x=1 and square the thickness of the disk, which is ((x^2)-0) In every disk problem, you will need to square the “thickness” Step 4) multiply everything by pie. It should look like this: from x=0 to x=1, ((x^2)-0)^2 dx all multiplied by pie The answer should be: pie/5

6
Find the volume of the solid generated when the curve y=x^2 between x=1, x=2 is rotated around the y-axis Step 1) Sketch a line segment parallel to axis of revolution. This is the height of a cylinder.

7
Step 2) Connect this segment perpendicular to the axis of revolution. This is the radius of a cylinder. Step 3)Find the limits of integration. If rotating around x-axis, then it will be dy. If rotating around y-axis, then it will be dx. Step 4) Integrate using Surface Area= (2)(r)(pie)

8
So, it would be: 2pie from 1 to 2 of (radius)(height) dx radius=(x) & height=(x^2-0) The answer should be :15pie/2

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google