Regions between surfaces

Question

a. Find the volume of the solid region.

 

The solid above the parabolic region R={(x,y): 0 ≤ x ≤ 1, 0 ≤ y ≤ 1-x²} and between the planes z = 1 and z = 2-y

 

b. Find the volume of the solid using triple integrals

 

The solid bounded by the surfaces z = e^y and z = 1 over the rectangle {(x,y): 0 ≤ x ≤ 1, 0 ≤ y ≤ ln2}

 

Answer 1

a. ∫₀¹∫₀^{1-x^2}(2-y-1)dxdy=2/5

 

b. ∫₀¹∫₀^ln2∫₁^{e^y}dxdydz=1-ln2