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प्रश्न
Which expression is the integration-by-parts form for a product \(f(x)g(x)\)?
पर्याय
\[\int f(x)g(x)\,dx=f(x)g(x)-\int f'(x)g'(x)\,dx\]
\[\int f(x)g(x)\,dx=f(x)\int g(x)\,dx-\int\left[f'(x)\int g(x)\,dx\right]dx\]
\[\int f(x)g(x)\,dx=f'(x)\int g(x)\,dx+\int\left[f(x)\int g(x)\,dx\right]dx\]
\[\int f(x)g(x)\,dx=g(x)\int f(x)\,dx-\int\left[g'(x)\int f(x)\,dx\right]dx\]
MCQ
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उत्तर
Take \(u=f(x)\) and \(dv=g(x)\,dx\) in \(\int u\,dv=uv-\int v\,du\). Thus \(du=f'(x)\,dx\) and \(v=\int g(x)\,dx\), giving the stated expression.
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