MHT CET202411 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
If x [-1,1] , then the value of e ^ ⁻¹ x ( x+ 1-x^2 1-x^2 ) d x is
Options
- Ae ^ ⁻¹ x + c , where c is constant of integration.
- Be ^ ⁻¹ x x+ c , where c is constant of integration.
- Ce ^ ⁻¹ x x+ c , where c is constant of integration.
- De ^ ⁻¹ x x+ c , where c is constant of integration.
Correct answer
D. e ^ ⁻¹ x x+ c , where c is constant of integration.
Step-by-step solution
aligned & Put ⁻¹ x= t 1 1-x^2 ~d x= dt & e ^ ⁻¹ x ( x+ 1-x^2 1-x^2 ) d x= e ^ t ( t + t ) dt & =e^t t + c & =x e ^ ⁻¹ x + c aligned