Question

1. Evaluate (𝑥 − 3) 𝑑 where = , , − 1 ≤ ≤ 1, 0 ≤ ≤ 2, 0 ≤ ≤ 1 }.

Answer 1

$\int_z\int_y\int_x(x-3)dxdydz\\\int_0^1\int_0^2\int_{-1}^1(x-3)dxdydz\\ \int_0^1\int_0^2x^2-3x|_{-1}^1dydz\\\int_0^1\int_0^2-6dydz\\\int_0^1(-6y|_0^2)dz\\\int_0^1-12dz=-12z|_0^1=-12\\$