MathCastle
Multivariable CalculusEasyChange of Variables & the Jacobian

Change of Variables & the Jacobian · Easy problem

Use spherical coordinates, with volume element dV=ρ2sin⁡ϕ dρ dϕ dθdV = \rho^2\sin\phi\,d\rho\,d\phi\,d\theta, to find the volume of the solid 0≤ρ≤30 \le \rho \le 3, 0≤ϕ≤π20 \le \phi \le \dfrac{\pi}{2}, 0≤θ≤2π0 \le \theta \le 2\pi.