If dx=-x +a, then a is equal to : - Vidyadip

MCQ

If $\int\text{x}\sin\text{x dx}=-\text{x}\cos\text{x}+\text{a},$ then a is equal to :

✓
$\sin\text{x}+\text{C}$
B
$\cos\text{x}+\text{C}$
C
$\text{C}$
D
None of these.

✓

Answer

Correct option: A.

$\sin\text{x}+\text{C}$

$\int\text{x}\sin\text{x dx}=-\text{x}\cos\text{x}+\text{a}$
$\text{I}=\int\text{x}\sin\text{x dx}$
$\text{I}=\text{x}\int\sin\text{x dx}-\int\Big(\frac{\text{dx}}{\text{dx}}\int\sin\text{x dx}\Big)\text{dx}$
$\text{I}=-\text{x}\cos\text{x}+\int\cos\text{x dx}$
$\text{I}=\text{x}\cos\text{x}+\sin\text{x}+\text{C}$
$\text{a}=\sin\text{x}+\text{C}$

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