Embibe Experts Solutions for Exercise 4: Assignment

Let $f\left(x\right)=\min \left({\cos }^{-1}\left(\cos x\right), {\cot }^{-1}\left(\cot x\right)\right), x\in (\pi , 2\pi )$ then which of the following statements are correct?

The three curves $y=\sqrt{x}, x=-\sqrt{y}$ and $x^2+y^2=2$ are given then the area

Two curves $f\left(x\right)=\cos x$ and $g\left(x\right)=1+\sin 2x,$ where $x\in \left(0, \frac{3\pi }{2}\right)$ are given then

If area bounded by the line $y=x,$ curve $y=f\left(x\right),$ ($f\left(x\right)>x,$ for all $x>1$) and the lines $x=1, x=t$ is $\left(t+\sqrt{1+t^2}\right)-\left(1+\sqrt{2}\right)$ for all $t>1,$ then

The area of region represented by $|x-y|\le 2$ and $x^2+y^2\le 4,$ is $(a\pi +b)$ sq. units then value of

The area enclosed between $y={\tan }^{-1}x, y={\cot }^{-1}x$ and $y$ axis in first quadrant is $A$ sq. units. Then $A$ is equal to

The area enclosed by the parabola $ay=3\left(a^2-x^2\right)$ and the $x$ axis is $f\left(a\right)$ square units then

The area of the region represented by the linear inequations $\left|x\right|+\left|y\right|\le 2; \left|x\right|\le 1$ and $\left|y\right|\ge 1$ is. $A$ square units, then