Question

Sketch the region bounded by the graphs of the functions, and find the area of the region.

Answer 1

Step 1:

The functions are and .

Region bounded is : .

Graph:

Graph the functions are and .

Shade the region bounded by the curves between  and .

Note: The region shaded in blue color is the required area of region.

Answer 2

Contd.....

Step 2:

Definite integral as area of the region:

If  and  are continuous and non-negative on the closed interval ,

then the area of the region bounded by the graphs of  and  and the vertical lines  and  is given by

.

Observe the graph:

Upper curve is .

Lower Curve is .

The vertical lines are  and .

Area of the region is .

Let .

Apply derivative on each side.

Substitute and in the integral.

Substitute .

Area of the region is 0.316 sq-units.

Answer 3

Contd.....

Solution:

Graph the region of graph of  and between  and  is

Area of the region is 0.316 sq-units.