For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . Consider the following: I. du dx = -v II. dv dx = -u Which of the above is/are correct?

Step-by-step solution

Given u = e^x x , dx and v = e^x x , dx . Differentiating both sides with respect to x , we get: du dx = e^x x dv dx = e^x x Evaluating the integrals, we have: u = e^x 2 ( x + x) + C₁ v = e^x 2 ( x - x) + C₂ Comparing the derivatives with u and v , it is clear that: du dx -v dv dx -u Therefore, neither statement I nor statement II is correct.