EXERCISE

The area of the region $\left\{(x, y) : x^2 + y^2 \le 1 - x\right\}$, using the method of integration is$\frac{a\mathrm{\pi }}{b}$, find $a+b$.

Find the area of the region bounded by the parabola $y=x^2+1$ and the lines $y=x, x=0$ and $x=2.$

Find the value of $k$, if the area of the triangle formed by negative x-axis, the tangent, and normal to the circle $x^2+y^2=9$ at $\left(-1,2\sqrt{2}\right)$ is $9\sqrt{k}$

Given curve $y={\cos }^2 x, 0 \le x \le \frac{\mathrm{\pi }}{2}$ and if the area included between the curve and the coordinate axes is $\frac{\mathrm{\pi }}{k}$ square units, find the value of $k$.

If the area of the region bounded by the curve $y=\left|x+4\right|, x=-6$ and $x=0$ is $k$ sq. units, then the value of $k$ is

Draw a rough sketch of the curves$y=(x-1{)}^2$ and $y=\left|x-1\right|$. Also find the area of the region bounded by these curves.

Find the area of the region $(x, y) ; 0 \le y\le x^2 + 1, 0\le y\le x + 1, 0\le x\le 2)$ .

If the area enclosed by the curve $y=\sin \left(x\right)$ and the $x-axis$ between $x=0$ to $x=2\pi$ be $k$ sq. units, then the value of $k$ is