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AP EAMCET201823 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual

If f(x)= cosec ^5 x d x , then f ( 4 )=

Options

  1. A- 1 4 [3 2 -5 ( 2 +1)]+c
  2. B- 1 8 [5 2 -3 ( 2 +1)]+c
  3. C- 1 8 [7 2 +3 ( 2 +1)]+c
  4. D1 8 [5 2 + ( 2 +1)]+c

Correct answer

C. - 1 8 [7 2 +3 ( 2 +1)]+c

Step-by-step solution

aligned & f(x)= cosec ^5 x d x= cosec ^2 x cosec ^3 x d x & = cosec ^3 x(- x)- - x 3 cosec ^2 x & (- cosec x x) d x & =- x cosec ^3 x-3 ^2 x cosec ^3 x d x & =- x cosec ^3 x-3 ( cosec ^2 x-1 ) cosec ^3 x d x & =- x cosec ^3 x-3 cosec ^5 x d x+3 cosec ^3 x d x & f(x)=- x cosec ^3 x-3 I+3 I₁ & 4 f(x)= x cosec ^3 x+3 I₁ & I₁= cosec ^3 x d x & = cosec x cosec ^2 x d x aligned aligned & = cosec x(- x)- - x (- cosec x x) d x & =- cosec x x- ^2 x cosec x d x & =- cosec x x- ( cosec ^2 x-1 ) cosec x d x & =- cosec x x- cos

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