Choose the correct answer in Exercise : If f(x)= ^ x _ 0 t dt, th… - Vidyadip

MCQ

Choose the correct answer in Exercise : $\text{If}\ \text{f}(\text{x})=\int^{\text{x}}_{0}\text{t}\sin\text{t}\ \text{dt}$, then $\text{f}\text{(x)}$ is

A
$\cos\text{x}+\text{x}\sin\text{x}$
✓
$\text{x}\sin\text{x}$
C
$\text{x}\cos\text{x}$
D
$\sin\text{x}+\text{x}\cos\text{x}$

✓

Answer

Correct option: B.

$\text{x}\sin\text{x}$

$\text{f}\text{(x)}=\int\limits_{0}^{\text{x}}\text{t}\sin\text{t}\ \text{dt}$
$\therefore\text{f}\ '\text{(x)}=\text{x}\sin\text{x}\ $
$\big[\therefore$ of first fundamental theorem$\big]$
$\text{f}\text{(x)}=\int\limits_{0}^{\text{x}}\text{t}\sin\text{t}\ \text{dt}$
$\therefore\text{f}\ '\text{(x)}=\text{x}\sin\text{x}\ \ $
$\big[\therefore$ of first fundamental theorem$\big]$

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