Question Detail
Question
Integrate ∫ ecos x sin x dx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
We can solve this integral using u-substitution.Let u = cos x.Then, differentiate u with respect to x: du/dx = -sin x.This means du = -sin x dx, or sin x dx = -du.Substitute u and -du into the integral:∫ eu (-du) = -∫ eu duThe integral of eu with respect to u is eu.So, we have -eu + C.Substitute back u = cos x:-ecos x + C.
Hint
Consider 'cos x' as the substitution variable.