Answer:
the volume of the solid is V=1/6
Step-by-step explanation:
The solid S has a triangular cross section in the xy-plane with sides of length L=1. The boundaries are
x=0
y=0
y= 1-x
Since each cross section perpendicular to the x axis ( parallel to the yz-plane) is a square then:
z=x
then the volume of the solid will be
V= ∫dV=∫∫∫dxdydz ∫₀¹(∫₀¹⁻ˣ dy)(∫₀ˣdz)dx = ∫₀¹ (1-x)*x dx = ∫₀¹ (x-x²) dx = [(1/2)x²-(1/3)x³] |₀¹ = 1/2 - 1/3 = 1/6
V=1/6
