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Using properties evaluate the following definite integrals int_0^(pi/2) cos^2x dx

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Solution :LET I = `int_0^(pi/2) cos^2 x dx` ____(a)
Then I = `int_0^(pi/2) cos^2 (pi/2-x)dx`
=`int_0^(pi/2) sin^2 x dx` ____(B)
(a)+(b)
`gt2I = int_0^(pi/2) (cos^2x+sin^2x)dx`
=`int_0^(pi/2) dx = [x]_0^(pi/2) = pi/2-0 = pi/2`
THUS, I = `pi/4`


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