Question

Find the volume of the region bounded above by the plane z = y/2 and below by the rectangle.

R ∶ 0 ≤ x ≤ 4,0 ≤ y ≤ 2

Answer 1

V= $\int_0^4 dx \int_0^2 dy \int_0^{y/2}dz= \int_0^4 dx \int_0^2 \frac y2 dy =$

$\int_0^4 dx \frac{y^2}{4}|_0^2= \int_0^4 dx =4$

Answer: V=4.