1.

Find the following integrals. int_0^(pi/2)frac(sinx)(1+cos^2x)dx

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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