Question

If $\int \left(u\frac{dv}{dx}\right)dx=uv-\int wdx$, then $w=$

• A. $\frac{du}{dx}\frac{dv}{dx}$
• B. $v\frac{du}{dx}$
• C. $\frac{d}{dx}\left(uv\right)$
• D. $u\frac{dv}{dx}$

Answer 1

The correct option is B $v\frac{du}{dx}$

Given,

$\int \left(u\frac{dv}{dx}\right)dx=uv-\int wdx$

it is called as, product rule integration,

$\int u.vdx=u\int vdx$ $-\int (\frac{du}{dx}\int vdx)dx$

$\int \left(u\frac{dv}{dx}\right)dx$

$=uv-\int v\frac{du}{dx}dx$

$\therefore w=v\frac{du}{dx}$