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Find the following integrals. int_0^(pi/2)frac(sinx)(1+cos^2x)dx |
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Answer» SOLUTION :Put COSX = 1. Then dt = -sinx dx `gt sinx dx = -dt` ALSO X = 0 `gt t = 1` and x = `pi/2 gt t = 0 therefore `int_0^(pi/2) sinx/(1+cos^2 x) dx = int_1^0 (-dt)/(1+t^2)` =`-[tan^-1 t]_1^0 = -[0-pi/4] = pi/4` |
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