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?

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Correct answer: D. Neither I nor II

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) + C_1 v = e^x 2 ( x - x) + C_2 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.

NDA Mathematics Question (2025) — Solution

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