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