MHT CET202519 Apr 2025Morning ShiftMathematicsIndefinite IntegrationActual
e ^ 2030 x - e ^ 2029 x e ^ 2028 x - e ^ 2027 x ~d x= .
Options
- Ax^2 2 +c , where c is the constant of integration
- Bx+c , where c is the constant of integration
- Cx^3 3 +c , where c is the constant of integration
- Dx 3 +c, where c is the constant of integration
Correct answer
C. x^3 3 +c , where c is the constant of integration
Step-by-step solution
The integral simplifies using the exponential and logarithmic identity e^ a x = x^a : I = x²⁰³⁰ - x²⁰²⁹ x²⁰²⁸ - x²⁰²⁷ dx Factoring gives x²⁰²⁹(x - 1) x²⁰²⁷(x - 1) = x^2 for x 1 . Integrating x^2 yields x^3 3 + c , matching option C .