MCQ
$f\left( x \right) = \int\limits_0^x {{e^x}\,{{\sin }^{ - 1}}(x - 1)\ln x\,dx(x > 0),} $ then
- A$f(x)$ has one local minima
- ✓$f(x)$ is an increasing function
- C$f(x)$ has one local maxima
- D$f(x)$ is a decreasing function
✓
Answer
Correct option: B.
$f(x)$ is an increasing function
b
$f(x)$ is defined when $-1 \leq x-1 \leq 1$ and $ x>0$
$f(x)$ is defined when $-1 \leq x-1 \leq 1$ and $ x>0$
$\Rightarrow x \in(0,2]$
${f^\prime }(x) = {e^x}{\sin ^{ - 1}}(x - 1)\ln x$
$f(x)$ is an increasing function.
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