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MHT CET202314 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

If I = d x (x- a ) (x- b ) , then I is given by

Options

  1. A1 ( b - a ) | (x- a ) (x- b )|+ c where c is a constant of integration.
  2. B| (x-a) (x-b) |+c , where c is a cónstant of integration.
  3. C1 ( b - a ) | (x- a ) (x- b ) |+ c , where c is a constant of integration.
  4. D1 ( b - a ) | (x- b ) (x- a ) |+ c , where c is a constant of integration.

Correct answer

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

Step-by-step solution

aligned & I = d x (x- a ) (x- b ) & = 1 ( b - a ) (x- a )-(x- b ) (x- a ) (x- b ) d x & = 1 ( b - a ) 1 (x- a ) (x- b ) [ (x- a ) (x- b ) & = 1 ( b - a ) [ (x- b )- (x- a )] d x & = 1 ( b - a ) [ | (x- b )|- | (x- a )|]+ c & = 1 ( b - a ) | (x- b ) (x- a ) |+ c aligned

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