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AP EAMCET201825 Apr 2018Morning ShiftMathematicsIndefinite IntegrationActual

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

Options

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

Correct answer

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

Step-by-step solution

Given: f x = ∫ cosec 5 x   d x = ∫ cosec 3 x I cosec 2 x II d x = cosec 3 x - cot x - ∫ - 3 cosec 3 x cot x - cot x d x = - cosec 3 x cot x - ∫ 3 cosec 3 x cot 2 x d x = - cosec 3 x cot x - ∫ 3 cosec 3 x cosec 2 x - 1 d x = - cosec 3 x cot x - 3 ∫ cosec 5 x d x + 3 ∫ cosec 3 x d x = - cosec 3 x cot x - 3 f x + 3 ∫ cosec 3 x d x ⇒ 4 f x = - cosec 3 x cot x + 3 ∫ cosec 3 x d x ⇒ 4 f x = - cosec 3 x cot x + 3 I     . . . i Now, I = &#8747

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