Question

The function $f\left(x\right)={\int }_0^x\sqrt{1-t^4}dt$ is such that

• A. it is defined on the interval $[-2,2]$
• B. it is an increasing function in $(-1,1)$
• C. it is an even function
• D. the point $(1,1)$ is the point of inflection

Answer 1

The correct option is B it is an increasing function in $(-1,1)$

$\begin{array}{c}f\left(x\right)={\int }_0^x\sqrt{1-t^4}dt\\ f^{\prime }\left(x\right)=\sqrt{1-x^4}>0\forall x\in \left(-1,1\right)\\ f\left(x\right)isincrea\sin gfunction.\\ OptionBiscorrectanswer.\end{array}$