R D Sharma Solutions for Chapter: Areas of Bounded Regions, Exercise 1: EXERCISE

The area of the region bounded by the line$y-1=x$, the $x-$ axis and the lines $x=-2$ and $x=3$ is given by $p$ square units. Find $p.$

Find the area of the region bounded by the parabola $y^2=4ax$ and the line $x=a$.

[Write the value without units]

Find the area lying above the $x$-axis and under the parabola $y=4x-x^2$.

[Write the value without units]

Draw a rough sketch of the graph of the curve $\frac{x^2}{4}+\frac{y^2}{9}=1$ and evaluate the area of the region under the curve and above the $x$-axis.

[Enter the value excluding the units]

Using integration, find the area of the region bounded by the line $2y=5x+7, x$-axis and the lines $x=2$ and $x=8$. [Write answer without units]

Using integration, find the area of the region bounded by the following curves, after making a rough sketch: $y=1+\left|x+1\right|, x=-2, x=3, y=0$.

[Enter the value excluding units]

Find the area bounded by the curve $y=\cos x, x$ axis and the ordinates $x=0$  and $x=2\mathrm{\pi }$.

[Enter the value excluding units]

Find the area enclosed by the curve $x=3 \cos t, y=2\sin t$