\(∈t e x (f(x) - f'(x))dx = (x),\) then the value..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep."> \(∈t e x... - Solved | MCA Prep" /> \(∈t e x (f(x) - f'(x))dx = (x),\) then the value..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." /> \(∈t e x... - Solved | MCA Prep" /> \(∈t e x (f(x) - f'(x))dx = (x),\) then the value..." - Step-by-step solution, answer key, and detailed explanation on MCA Prep." />
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Question 24

Mathematics Definite Integrals Hard

If&nbsp;<span class="math-tex">\(\int e^x (f(x) - f'(x))dx = \phi(x),\)</span> then the value of&nbsp;<span class="math-tex">\(\int e^x f(x)dx\)</span> is

(A) ϕ(x) + e<sup>x</sup> f(x)
(B) ϕ(x) - e<sup>x</sup> f(x)
(C) <span class="math-tex">\(\frac 1 2 \left[\phi (x) + e^x f(x)\right]\)</span>
(D) <span class="math-tex">\(\frac 1 2 \left[\phi (x) + e^x f'(x)\right]\)</span>
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Correct Solution: Option C

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