given f(x) and g(x).
f(x)=sin(pi x) & g(x)=(2x^3)-(8x)

a) write and evaluate an integral expression in terms of x to represent the area of region R which is the region bounded between the functions.

b) find the volume for the region R when rotated about the line y=-4. Round to the nearest thousandth

c) Given that the horizontal line y=-3 intersects the region R, what is the area below this line?

d) What is the volume for a solid whose base is R formed by rectangular cross-sections with a height of (1/2)x.

e) The vertical line x=(1/2) intersects the region R. What is the area of the region on the interval [0,1/2]