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Evaluate the definite integrals intpi...

Evaluate the definite integrals `intpi/6pi/4cose c""x""dx`

Text Solution

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`I= int_(pi//6)^(pi//4) " cosec "x dx`
`=[log |"cosec"x-cot x|]_(pi//6)^(pi//4)`
`=log |"cosec ".(pi)/(4)-cot .(pi)/(6)|`
`=log |sqrt(2)-1|-log |2-sqrt(3)|`
`=log |(sqrt(2)-1)/(2-sqrt(3))|`
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