Area Under the Curves

The area of the region bounded by the parabola (y $$-$$ 2)² = (x $$-$$ 1), the tangent to it at the point whose ordinate is 3 and the x-axis is :

The area, enclosed by the curves $$y = \sin x + \cos x$$ and $$y = \left| {\cos x - \sin x} \right|$$ and the lines $$x = 0,x = {\pi \over 2}$$, is :

The area enclosed by y² = 8x and y = $$\sqrt2$$ x that lies outside the triangle formed by y = $$\sqrt2$$ x, x = 1, y = 2$$\sqrt2$$, is equal to:

The area of the region S = {(x, y) : y² $$\le$$ 8x, y $$\ge$$ $$\sqrt2$$x, x $$\ge$$ 1} is

The area bounded by the curve y = |x² $$-$$ 9| and the line y = 3 is :

The area of the region bounded by y² = 8x and y² = 16(3 $$-$$ x) is equal to:

The area of the region given by $$A=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\}$$ is :

Let the locus of the centre $$(\alpha, \beta), \beta>0$$, of the circle which touches the circle $$x^{2}+(y-1)^{2}=1$$ externally and also touches the $$x$$-axis be $$\mathrm{L}$$. Then the area bounded by $$\mathrm{L}$$ and the line $$y=4$$ is:

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y^a is $${{364} \over 3}$$, is equal to :

The area bounded by the curves $$y=\left|x^{2}-1\right|$$ and $$y=1$$ is