Solución

a. f(ρ,θ,ϕ)=ρsenϕ(cosθ+senθ)f(\rho, \theta, \phi) = \rho sen\phi(cos\theta + sen\theta),
E={(ρ,θ,ϕ)∣1≤ρ≤2,0≤θ≤π,0≤ϕ≤π/2}E = \bigg\lbrace (\rho, \theta, \phi)|1 \le \rho \le 2, 0 \le \theta \le \pi, 0 \le \phi \le \pi/2\bigg\rbrace
b.
∫0π∫0π/2∫12ρ3cosϕsenϕdρdϕdθ=15π8\int_0^{\pi}\int_0^{\pi/2}\int_1^2 \rho^3 cos\phi sen \phi d\rho d\phi d\theta = \frac{15\pi}{8}