Question

Integration Procedures (Integration by Parts)

∫ θ cosθ dθ

Answer 1

$$\int\theta\cos \theta d\theta$$

Integration by Parts

$$\int u dv=uv-\int v du$$

$$u=\theta , du=d\theta$$

$$dv=\cos \theta d\theta, v=\int \cos \theta d\theta=\sin \theta$$

$$\int\theta\cos \theta d\theta=\theta\sin \theta-\int\sin \theta d\theta$$

$$=\theta\sin \theta+\cos \theta +C$$

$$\int\theta\cos \theta d\theta=\theta\sin \theta+\cos \theta +C$$