Question

Trick to integrate (sin²θ):

a) Apply the power reduction formula.

b) Use the double-angle identity.

c) Apply integration by parts.

d) This integral cannot be solved.

Answer 1

To integrate sin²θ, the power reduction formula, which expresses sin²θ as (1/2)(1 - cos 2θ), is the most effective technique.

Step-by-step explanation:

The best option to integrate sin²θ is to apply the power reduction formula. This method involves using trigonometric identities to rewrite the integrand in a form that's easier to integrate.

One common identity used for power reduction is cos 2θ = 1 - 2 sin² θ, which can be rearranged to sin² θ = (1/2)(1 - cos 2θ). This transformation simplifies the integral of sin² θ into an integral that can be easily solved by basic integration techniques.