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Evaluate the definite integralsint0^(pi...

Evaluate the definite integrals`int_0^(pi/4)(sinx+cosx)/(9+16sin2x)dx`

Text Solution

Verified by Experts

Let `sinx-cosx=t`
thus,
`I=intdt/(9+16(1-t^2))`
`=1/16intdt/(25-t^2)`
`=1/4[1/10log|(5+4t)/(5-4t)|]`
now, for range -1 to 0
we have
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