The value of _ ^ x kx ;dx is - Vidyadip

MCQ

The value of $\int_{}^{} {x\sin kx\;dx} $is

A
$\frac{{\sin kx}}{k} + c$
B
$\frac{{\cos kx}}{k} + c$
C
$\frac{{\sin x}}{k} + c$
✓
$ - \frac{{x\,\cos kx}}{k} + \frac{{\sin kx}}{{{k^2}}} + c$

✓

Answer

Correct option: D.

$ - \frac{{x\,\cos kx}}{k} + \frac{{\sin kx}}{{{k^2}}} + c$

d
(d) $I = \int_{}^{} {x\sin kx\,dx} = \frac{{ - x\cos kx}}{k} + \frac{{\sin kx}}{{{k^2}}} + c$

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