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The value of the integral overset(pi//4)...

The value of the integral `overset(pi//4)underset(0)int sin^(-4)x dx`, is

A

`-(8)/(3)`

B

`(3)/(2)`

C

`(8)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` l = int_(-pi//4)^(pi//4) sin^(-4) x dx = int _(-pi//4)^(pi//4) x^(4) dx`
Put ` cot x = t rArr - 1^(2) x dx = dt`
` :. l = int_(-1)^(1) (1+t^(2)) dt = -2 int_(0)^(1) (1+ t^(2))dt`
` = - 2 [ t+(t^(3))/3]_(0)^(1) = - 2 [ 1+1/3] = - 8/3`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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