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Using properties evaluate the following definite integrals, evaluate the following: int_0^(pi/2) (sinx-cosx)/(1+sinx cosx) dx

Answer»

Solution :`int_0^(pi/2) (sinx-cosx)/(1+sinx cosx) dx`____ (a)
Then `I = int_0^(pi/2) (SIN(pi/2-x) -cos(pi/2-x))/(1+sin(pi/2-x) cos(pi/2-x)) dx`
int_0^(pi/2) (cosx-sin)/(1+cosx sinx) dx` ____(b)
(a)+(b)
`GT 2I = int_0^(pi/2) 0/(1+sinx cosx) dx` = 0
`gt I` = 0.


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