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By using the properties of definite inte...

By using the properties of definite integrals, evaluate the integrals`int_0^(pi/2) cos^2x dx`

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`I=int_0^(pi/2) cos^2xdxdx .............. (1)`
⇒`I=int_0^(pi/2) cos^2(π/2​−x)dx,`
⇒`I=int_0^(pi/2) ​​sin^2xdx ` .....(2)
Adding (1) and (2), we obtain `2I=int_0^(pi/2) ​​(sin^2x+cos^2x)dx​`
⇒`2I=int_0^(pi/2) ​​1⋅dx​`
⇒`2I=π/2​​`
...
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