Question

integration of sin²x​

Answer 1

Answer:

This integral cannot be evaluated by the direct formula of integration, so using the trigonometric identity of half angle sin2x=1–cos2x/2,

we have

I=∫(1–cos2x2)dx

⇒I=1/2∫(1–cos2x)dx

⇒I=1/2∫1dx–12∫cos2xdx

Using the integral formula ∫coskxdx=sinkxk+c, we have

∫sin2xdx=1/2x–1/2sin2x2+c⇒∫sin2xdx=1/2x–1/4sin2x+c