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int(0)^(pi//2)sin^(2)xdx=?...

`int_(0)^(pi//2)sin^(2)xdx=?`

A

`(pi)/(3)`

B

`(pi)/(4)`

C

`(pi)/(2)`

D

`(2pi)/(3)`

Text Solution

AI Generated Solution

To solve the integral \( \int_{0}^{\frac{\pi}{2}} \sin^2 x \, dx \), we can use the identity for \( \sin^2 x \). ### Step-by-Step Solution: 1. **Use the identity for \( \sin^2 x \)**: We know that: \[ \sin^2 x = \frac{1 - \cos(2x)}{2} ...
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