Question

evaluate integral (sin^2(t) dt) from 0 to 2pi?

Answer 1

\[\int\limits_{0}^{2\pi}\sin^2(t)dt\]

Answer 2

sin^2 has a simpler version ...

consider the identity of cos(2t) to find a suitable substution for sin^2(t)

Answer 3

\[\cos(2t)=1-2\sin^2(t)\rightarrow \sin^2(t)=\frac{ 1-\cos(2t) }{ 2 }\]

Answer 4

That is called power reduction formula.
It's good to know them to make integration easier.

Answer 5

Can you take it from here?

Answer 6

ys

Answer 7

good luck

Answer 8

:)

Answer 9

\[\int\limits \sin ^2(t) \, dt=\frac{t}{2}-\frac{1}{4} \sin (2 t) \]\[\int\limits_0^{2 \pi } \sin ^2(t) \, dt=\pi \]\[\left(\frac{t}{2}-\frac{1}{4} \sin (2 t)\text{/.}\, t\to 2 \pi \right)-\left(\frac{t}{2}-\frac{1}{4} \sin (2 t)\text{/.}\, t\to 0\right)=\pi \]