Step 1:

The area bounded by the function is , -axis and the lines , .

Area of the region between two curves:

If and  are continuous on and for all in , then the area of the region biunded by the graphs of and and the vertical lines and is.

Here, , , and .

Graph the functions and on .

Observe the graph: \ \

The two functions on interval . \ \

Step 2:

Substitute , and in .

Apply power rule of integration: .

.

Area bounded by the graph is .

Solution:

Area bounded by the graph is .

(1)(b)

Step 1:

The area bounded by the function is , -axis and the lines , .

Area of the region between two curves:

If and  are continuous on and for all in , then the area of the region biunded by the graphs of and and the vertical lines and is.

Here, , , and .

Graph the functions and on .

Observe the graph: \ \

The two functions on interval the . \ \

Step 2:

Substitute , and in .

Apply formula: .

.

Area bounded by the graph is .

Solution:

Area bounded by the graph is .

2

Step 1:

The functions are  and .

Area of the region between two curves:

If and  are continuous on and for all in , then the area of the region biunded by the graphs of and and the vertical lines and is .

Graph the functions and .

Observe the graph:

The two functions are intersect at the points and . and .

on the interval .

The two curves are intersected at , and .

Step 2:

Find the area of the region.

Substitute , and in .

Apply power rule of integration: .

.

Area bounded by the graph is .

Solution:

Area bounded by the graph is .