Evaluate the integrals using u-substitution:

Question

Evaluate the integrals using u-substitution:

∫theta (⁴√1-theta)²dtheta

Answer 1

∫ θ ⁴√(1 - θ²)dθ

Let u = 1 - θ². Then du = -2θdθ. So, θdθ = -(1/2)du.

We have -(1/2) ∫ u^1/4du = -(2/5)u^5/4 + C = -(2/5)(1 - θ²)^5/4 + C