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MHT CET20227 Aug 2022Evening ShiftMathematicsIndefinite IntegrationActual

(3-x) 4-x d x= (Where C is a constant of integration.)

Options

  1. A2 3 (4-x)^ 3 / 2 + 2 5 (4-x)^ 5 / 2 +C
  2. B- 2 5 (4-x)^ 5 / 2 + 2 3 (4-x)^ 3 / 2 +C
  3. C2 3 (4-x)^ 3 / 2 - 2 5 (4-x)^ 5 / 2 +C
  4. D2 5 (4-x)^ 5 / 2 - 2 5 (4-x)^ 3 / 2 +C

Correct answer

C. 2 3 (4-x)^ 3 / 2 - 2 5 (4-x)^ 5 / 2 +C

Step-by-step solution

aligned & (3-x) 4-x d x & = (4-x)-1 4-x d x= (4-x)^ 3 2 -(4-x)^ 1 2 d x & = 2 5 (4-x)^ 5 / 2 + 2 3 (4-x)^ 3 / 2 +C & = 2 3 (4-x)^ 3 / 2 - 2 5 (4-x)^ 5 / 2 +C aligned

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