We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? =) Thank you!
1) Find the volume of the solid formed when the region bounded by curves y=x^3 + 1, x= 1, and y=0 is rotated about the x-axis.
My answer is 23/14.
2) Find the volume of the solid of revolution obtained by revolving the region bounded by y=1/x and the lines x=pi/8 and x=pi/2 around the x-axis.
I got 6/pi for this one.
3) Find the area bounded by the curves f(x)= x^3 + x^2 and g(x)= 2x^2 + 2x.
My answer: 5/12
Can you tell me if I did them wrong, and if I did do them wrong what I Did wrong?
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
x+y=4,x=5−(y−1) 2 ;