Advertisements
Advertisements
प्रश्न
Which expression is the integration-by-parts form for a product \(f(x)g(x)\)?
विकल्प
\[\int f(x)g(x)\,dx=f(x)g(x)-\int f'(x)g'(x)\,dx\]
\[\int f(x)g(x)\,dx=f(x)\int g(x)\,dx-\int\left[f'(x)\int g(x)\,dx\right]dx\]
\[\int f(x)g(x)\,dx=f'(x)\int g(x)\,dx+\int\left[f(x)\int g(x)\,dx\right]dx\]
\[\int f(x)g(x)\,dx=g(x)\int f(x)\,dx-\int\left[g'(x)\int f(x)\,dx\right]dx\]
MCQ
Advertisements
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.
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
