# Calculus

posted by .

alright. i need to write a definite integral for the volume and evaluate the integral for the region bounded by y=x^2, y=0, and x=1 revolved about the a) x-axis, b) the y-axis, c) x=2, and d) y=-2.
HELP!

Lets do the x=2 axis.

dV= pi rh dr where r is radius, h is height. r= x-1 dr=dx h= y=x^2
dV= PI (x-1)x^2 dx
Then integrate from x=1 to 2

So the idea is to draw the pic, make an incremental dV in terms of r and h, change those to x,y variables.

dV= PI r h dr
r= 6-y y goes from 0 to 1^2
dr= dy
h= 1-sqrt(y)
check that picture

## Similar Questions

1. ### MATH

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y - y3, x = 1, y = 1 (b) Revolved about the y-axis ?
2. ### Calculus AP

Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral …
3. ### calculus

using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1
4. ### Calculus check

The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but …
5. ### Calculus check and help

Let R be the region bounded by the curves y=lnx^2 and y=x^2-4 to the right of the y-axis. A. Find the area of R. B. Find the folume geneated when R is rotated about the line y=-4. C. Write, but do not evaluate the integral expression …
6. ### calculus

the region bounded by the graph f(x)=x(2-x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.
7. ### Calculus

The semicircular region bounded by the curve x=sqrt{9-y^2} and the y-axis is revolved about the line x=-3. The integral that represents its volume is V= âˆ« [a^b] f(y) dy What is f(y)?