An integral by symmetry

MediumCalculus~4m

Evaluate $\displaystyle\int_0^{\pi/2}\sin^2 x\,dx$ . Give a decimal to four places.

Show hints (2)+

Let $I=\int_0^{\pi/2}\sin^2$ . Show it equals $\int_0^{\pi/2}\cos^2$ via $x\mapsto\tfrac{\pi}{2}-x$ .
Add them: $2I=\int_0^{\pi/2}1\,dx$ .

Answer

Reveal answer →

0.7854 (± 0.001)

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