Application of ...

The area bounded by the parabola $$\mathrm{y}^{2}=4\mathrm{a}(\mathrm{x}+\mathrm{a})$$ and $$\mathrm{y}^{2}=-4\mathrm{a}(\mathrm{x}-\mathrm{a})$$ is

$$\sin x$$ & $$\cos x$$ meet each other at a number of points and develop symmetrical area. Area of one such region is

Let $$\displaystyle \mathrm{f}(\mathrm{x})=\min\{x+1,\ \sqrt{1-x}\}$$, then the area bounded by $$\mathrm{y}={f}({x})$$ and $${x}$$-axis is:

Area bounded by the curves $$\displaystyle \frac{y}{x}=\log x$$ and $$\displaystyle \frac{y}{2}=-x^{2}+x$$ equals:

The area bounded by the curves $$\mathrm{y}=2^{\mathrm{x}}$$,$$\mathrm{y}=2\mathrm{x}-\mathrm{x}^{2}$$ between the lines $$\mathrm{x}=0,\ \mathrm{x}=2$$ is

The area bounded by two branches of the curve $$(y-x)^{2}=x^{3} \& x=1$$ equals

Area bounded by $$x^{2}=4ay$$ and $$y=\displaystyle \frac{8a^{3}}{x^{2}+4a^{2}}$$ is:

Area bounded by the curves satisfying the conditions $$\displaystyle \frac{x^{2}}{25}+\frac{y^{2}}{36}\leq 1\leq\frac{x}{5}+\frac{y}{6}$$ is given by

The area of the region bounded by the curve y $$\displaystyle =\frac{16-x^{2}}{4}$$ and $$\displaystyle y=sec^{-1}[-sin^{2}x],$$ where [.] stands for the greatest integer function is:

The area of the smaller region in which the curve $$y=\left [ \frac{x^{3}}{100}+\frac{x}{50} \right ],$$ where[.] denotes the greatest integer function, divides the circle $$\left ( x-2 \right )^{2}+\left ( y+1 \right )^{2}=4,$$ is equal to