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MHT CET202415 May 2024Morning ShiftMathematicsIndefinite IntegrationActual

The value of d x 7+6 x-x^2 is equal to

Options

  1. A1 4 ( 1+x 7-x )+ c , (where c is a constant of integration)
  2. B1 8 ( 7-x 1+x )+ c ,( where c is a constant of integration)
  3. C1 4 ( 7-x 1+x )+ c , (where c is a constant of integration)
  4. D1 8 ( 1+x 7-x )+ c , (where c is a constant of integration)

Correct answer

D. 1 8 ( 1+x 7-x )+ c , (where c is a constant of integration)

Step-by-step solution

aligned 1 7+6 x-x^2 ~d x & = 1 7+6 x-x^2-9+9 ~d x & = 1 16- (x^2-6 x+9 ) d x & = 1 4^2-(x-3)^2 ~d x & = 1 2(4) | 4+(x-3) 4-(x-3) |+ c & = 1 8 | 1+x 7-x |+ c aligned

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