1 7 ( x 7 +10 )dx is equal to : - Vidyadip

MCQ

$\int\frac{1}{7}\sin\Big(\frac{\text{x}}{7}+10\Big)\text{dx}$ is equal to :

A
$\frac{1}{7}\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
B
$-\frac{1}{7}\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
✓
$\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$
D
$-7\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$

✓

Answer

Correct option: C.

$\cos\Big(\frac{\text{x}}{7}+10\Big)\text{C}$

Let $\text{I}=\int\frac{1}{7}\sin\Big(\frac{\text{x}}{7}+10\Big)\text{dx}$
$=\frac{1}{7}\int\sin\Big(\frac{\text{x}}{7}+10\Big)=\frac{1}{7}\frac{-\cos\Big(\frac{\text{x}}{7}+10\Big)}{\frac{1}{7}}$
$=-\cos\Big(\frac{\text{x}}{7}+10\Big)+\text{C}$

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