If $\frac{d}{d x} f(x)=x \cos x+\sin x$ and $f(0)=2$, then $f(x)=$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\frac{d}{d x} f(x)=x \cos x+\sin x

and

f(0)=2

, then

f(x)=

View answer and explanation

Correct option: C

x \sin x+2

Option C is correct because integrating x cos(x) + sin(x) results in x sin(x) + C, and using the initial condition f(0) = 2, we find that C = 2, so f(x) = x sin(x) + 2.

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\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx

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