The measurement ofthe area bounded by the coordinate axes and the curve y = log_e(x), is

• 1

• 2

• 3

• $\infty$

The area common to the curves y² = x and x² = y will be

• 1 sq unit

• $\frac{2}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{1}{4} \mathrm{sq} \mathrm{unit}$

• $\frac{1}{3} \mathrm{sq} \mathrm{unit}$

Area common to the circle x² + y² = 64 and the parabola y² = 12x is equal to

• $\left(\frac{16}{3}\right)\left(4\mathrm{\pi } + \sqrt{3}\right)$

• $\left(\frac{16}{3}\right)\left(8\mathrm{\pi } - \sqrt{3}\right)$

• $\left(\frac{16}{3}\right)\left(4\mathrm{\pi } - \sqrt{3}\right)$

• None of these

Area bounded by the curve y = x³, the x-axis and the ordinates x = - 2 and x = 1 is

• - 9

• $- \frac{15}{4}$

• $\frac{15}{4}$

• $\frac{17}{4}$

235.

Find the area of the region {(x, y) : x² $\le \mathrm{y} \le \left|\mathrm{x}\right|$}

• $\frac{1}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{4}{3} \mathrm{sq} \mathrm{unit}$

• $\frac{2}{3} \mathrm{sq} \mathrm{unit}$

• None of these

Determine the area included between the curve $\mathrm{y} {=}^2 \cos \left(\mathrm{x}\right), 0 \le \mathrm{x} \le \frac{\mathrm{\pi }}{2}$ and the axes.

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{2\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

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

• 1 sq units

• 2 sq units

• 3 sq units

• 4 sq units

Area of the region bounded by the parabola y = x² and the curve y = $\left|\mathrm{x}\right|$ is

• 3

• $\frac{1}{3}$

• 2

• $\frac{1}{2}$

The curve, for which the area of the triangle formed by X-axis, the tangent line at any point P and line OP is equal to a, is given by

• $\mathrm{y} = \mathrm{x} - {\mathrm{Cx}}^2$

• $\mathrm{x} = \mathrm{Cy} \pm \frac{{\mathrm{a}}^2}{\mathrm{y}}$

• $\mathrm{y} = \mathrm{Cy} \pm \frac{{\mathrm{a}}^2}{\mathrm{x}}$

• None of these

The area bounded by the curves y = x², y = - x² and y² = 4x - 3 is k, then the value of 6k is

• 2

• 3

• 0

• 4