Question Detail
Question
Integrate ∫ ecos x sin x dx.
Correct Answer
Option B is the correct answer.
Detailed Explanation
This integral can be solved using a simple substitution.Let u = cos x.Then, differentiate u with respect to x: du/dx = -sin x.This means sin x dx = -du.Substitute these into the integral:∫ ecos x sin x dx = ∫ eu (-du) = -∫ eu du.The integral of eu is eu.So, -∫ eu du = -eu + C.Substitute back u = cos x: -ecos x + C.This matches option B.
Hint
Consider a substitution where u is the exponent of e.