MHT CET202314 May 2023Evening ShiftMathematicsIndefinite IntegrationActual
If I = d x (x- a ) (x- b ) , then I is given by
Options
- A1 ( b - a ) | (x- a ) (x- b )|+ c where c is a constant of integration.
- B| (x-a) (x-b) |+c , where c is a cónstant of integration.
- C1 ( b - a ) | (x- a ) (x- b ) |+ c , where c is a constant of integration.
- 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