If I₁ = _e^ e^2 dx x and I₂ = ₁^2 e^x x , dx , then which one of the following is correct?

Step-by-step solution

I₁ = _e^ e^2 dx x Substituting x = t x = e^t dx = e^t dt When x = e , t = 1 When x = e^2 , t = 2 I₁ = ₁^2 e^t t dt Since the definite integral is independent of the variable of integration, I₁ = ₁^2 e^x x dx = I₂ I₁ - I₂ = 0 Answer: I₁ - I₂ = 0