Maths-

General

Easy

Question

# If x sin x dx = – x cos x + , then =

- sin x + c
- cos x + c
- x cos x + c
- cos x – sin x + c.

## The correct answer is: sin x + c

### To find the value of $α$

Let I=xsinxdx

Let $u=x$
$⇒du=dx$
$dv=sinxdx$
$⇒v=−cosx$
$I=−xcosx+cosxdx$
$I=−xcosx+sinx+c$
$I=xsinxdx=−xcosx+α$
Comparing with $I=−xcosx+sinx+c$ we have
$α=sinx+c$

$I=−xcosx+cosxdx$

$I=−xcosx+sinx+c$

$I=xsinxdx=−xcosx+α$

Comparing with $I=−xcosx+sinx+c$ we have

$α=sinx+c$

Therefore, the value of α is sinx+c

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