Question

Value of ∫uv dx,where u and v are function of x.

(a) \(\sum_{i=1}^n(-1)^i u_i v^{i+1}\)

(b) \(\sum_{i=0}^nu_i v^{i+1}\)

(c) \(\sum_{i=0}^n(-1)^i u_i v^{i+1}\)

(d) \(\sum_{i=0}^n(-1)^i u_i v^{n-i}\)

This question was posed to me in quiz.

I want to ask this question from Improper Integrals in chapter Integral Calculus of Engineering Mathematics

Answer 1

Right choice is (c) \(\sum_{i=0}^n(-1)^i u_i v^{i+1}\)

To explain I would say: Add constant automatically

Given, f(x)=\(\int uvdx=\sum_{i=0}^n (-1)^i u_i v^{i+1}\)