Triple integral calculator spherical

Apr 22, 2019 · 0 ≤ φ ≤ π 4 0 ≤ φ ≤ π 4. The other way to get this range is from the cone by itself. By first converting the equation into cylindrical coordinates and then into spherical coordinates we get the following, z = r ρ cos φ = ρ sin φ 1 = tan φ ⇒ φ = π 4 z = r ρ cos ⁡ φ = ρ sin ⁡ φ 1 = tan ⁡ φ ⇒ φ = π 4. Since the wavefunction depends on r, which is the spherical coordinate representing the distance from the origin, we use spherical coordinates to perform the integration because it is most convenient. And yes, this is a triple integral, $\int_0^{2\pi}d\phi\int_0^{\pi}\sin\theta d\theta\int_0^{\infty}r^2\Psi^*\Psi dr$. Triple integral in spherical coordinates (Sect. 15.6). Example Use spherical coordinates to find the volume of the region outside the sphere ρ = 2cos(φ) and inside the half sphere ρ = 2 with φ ∈ [0,π/2]. Solution: First sketch the integration region. I ρ = 2cos(φ) is a sphere, since ρ2 = 2ρ cos(φ) ⇔ x2+y2+z2 = 2z x2 + y2 +(z ...