Question

Evaluate the integral by making the given substitution. (Use C for the constant of integration.) sin3(θ) cos(θ) dθ , u = sin(θ) g

Answer 1

Evaluate int[sin^3(θ)cos(θ)dθ] with u = sin(θ)
du/dθ = cos(θ), dθ = du/cos(θ)

The integral becomes:
int[u^3•cos(θ)du/cos(θ)]
= int[u^3•du]
= u^4/4 + C

Substitute u = sin(θ) to get back a function of θ:
sin^4(θ)/4 + C