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Evaluate the definite integralsint(pi/6...

Evaluate the definite integrals`int_(pi/6)^(pi/4) cose cxdx`

Text Solution

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`I=int_(pi/6)^(pi/4) cosecx dx`
`=[log(cosecx-cotx]_(pi/6)^(pi/4)`
`=log(cosec(pi/4)-cot(pi/4))-log(cosec(pi/6)-cot(pi/6))`
`=log(sqrt2-1)-log(2-sqrt3)`
`=log{(sqrt2-1)/(2-sqrt3)}`
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