Posted by Megan on .
Sketch the region bounded by the curves y = x^2, y = x^4.
1) Find the area of the region enclosed by the two curves;
2) Find the volume of the solid obtained by rotating the above region about the xaxis;
3) Find the volume of the solid obtained by rotating the above region about the horizontal line with
equation y = 1 .

calculus 
drwls,
The region bounded by the two curves is between x = 1 and x = +1. Plot the two curves and you will see why.
1) Integrate (x^2  x^4)dx from x = 1 to x = 1
2) Integrate pi*y1^2  pi*y2^2 dx
= pi*(x^4  x^8)dx from x = 1 to x = 1.
y1(x) = x^2
y2(x) = x^4
3) Integrate pi[(1  y2)^2  (1  y1)^2]
dx from 1 to +1