The area bounded by the curve $y = x^2 + 1$ and the tangents to it drawn from the origin is

The area of the region bounded by the line $y=x$ and the curve $y=x^3$ is

The area of the smaller region enclosed by the curves $y^{2}=8x+4$ and $x^{2}+y^{2}+4\sqrt{3}x-4=0$ is equal to.

The area (in sq. units) of the region bounded by the lines $x=0, x=\frac{\pi}{2}$ and $f(x)=\sin x, g(x)=\cos x$ is

Let $C_{1}$ be the curve obtained by the solution of the differential equation $2xy \frac{dy}{dx} = y^{2} - x^{2}, x > 0$. Let the curve $C_{2}$ be the solution of $\frac{2xy}{x^{2} - y^{2}} = \frac{dy}{dx}$. If both the curves pass through $(1, 1)$,then the area enclosed by the curves $C_{1}$ and $C_{2}$ is equal to:

The area of the region bounded by the curve $y = \sin(\pi x)$ and the $X$-axis for $x \in [-1, 2]$ is . . . . . . sq. units.