Vinod Singh and Shweta Pawar Solutions for Chapter: Applications of Definite Integral, Exercise 3: Competitive Thinking

The area of the region bounded by the curves $y=\left|x-1\right|$ and $y=3-\left|x\right|$ is

The area bounded by curves $y=x^2, y=\frac{2}{\left(1+x^2\right)}$ in square units is

The area in $\left(\text{sq. units}\right)$ included between the parabola $y=\frac{x^2}{4a}$ and the curve $y=\frac{8a^3}{\left(x^2+4a^2\right)}$ is

The area in $\left(\text{sq. units}\right)$ of region $\left\{\left(x,y\right):x^2+y^2\le 1\le x+y\right\}$ is

The area of the region lying above $X$-axis, and included between the circle $x^2+y^2=2ax$ and the parabola $y^2=ax, a>0$ is

The area in $\left(\text{sq. units}\right)$ of the region described by $A=\{\left(x,y\right):x^2+y^2\le 1$ and $\left.y^2\le 1-x\right\}$ is

The area (in $\mathrm{sq}.\mathrm{units}$) of the region described by $\{\left(x,y\right):y^2\le 2x$ and $y\ge 4x-1\}$ is

The area enclosed (in square units) by the curve $y=x^4-x^2,$ the $X$-axis and the vertical lines passing through the two minimum points of the curve is