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If the integrating factor of $\frac{dy}{dx} + \left[(x^2 - 2x)\cos x + 2(x - 1)\sin x\right]y = x^2$ is $e^{f(x)}$, then $f(3) =$}

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Always look for exact differential patterns like $d(u \cdot v) = u \, dv + v \, du$ when dealing with long, intimidating integrals involving combinations of polynomials and trigonometric functions.

Updated On: Jul 9, 2026

$3\cos 3 + 4\sin 3$
$4\cos 3$
$3\sin 3$
$4\sin 3 + \cos 3$

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The Correct Option is C

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If the integrating factor of $\frac{dy}{dx} + \left[(x^2 - 2x)\cos x + 2(x - 1)\sin x\right]y = x^2$ is $e^{f(x)}$, then $f(3) =$}

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The Correct Option is C

Solution and Explanation

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