Question

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

Answer 1

Step 1:

The functions are and .

Graph:

Graph the functions are and .

Shade the region bounded by the curves in the intersection part.

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 .

Region bounded between and .

So the vertical lines are and .

Area of the region is .

Area of the region is 4.5 sq-units.

Solution:

Graph the region of graph of  and  is

Area of the region is 4.5 sq-units.