99 Percentile Qs Bank for JEE MainMathematicsIndefinite Integration

If ^2 x cosec ^4 x d x=- 1 3 ^3 x+k x-2 x+C , then k is equal to

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Correct answer

D. 1

Step-by-step solution

Let I= ^2 x cosec ^4 x d x aligned & = 1 ^4 x ^2 x d x= ^2 x+ ^2 x ^4 x ^2 x d x & = d x ^2 x ^2 x + d x ^4 x & .= ( ^2 x+ ^2 x ) d x ^2 x ^2 x + cosec ^2 x ) & = ( ^2 x+ cosec ^2 x ) d x & + cosec ^2 x (1+ ^2 x+ ^2 x ) & = x- x+ cosec ^2 x d x & = x- x- x- ^3 x 3 +C & =- 1 3 ^3 x+ x-2 ^2 x+C ^2 x d x aligned But it given that, aligned & I=- 1 3 ^3 x+k x-2 x+C k & =1 aligned

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