5)

Step 1:

The curve equations is and the -axis is equation is .

And the vertical boundaries are and .

The area of a region bounded by a graph of a function, the -axis, and two vertical boundaries can be determined directly by evaluating a definite integral.

If on , then the area of the region lying below the graph of , above the -axis, and between the lines and   is .

.

Step 2:

Since on , then the area of the region lying below the graph of , above the -axis, and between the lines and   is .

Apply the power rule in integration:.

square units.

Solution:

square units.

6) \ \

Step 1: \ \

The curve equation is and the -axis equation is . \ \

Formula for the area is . \ \

In this case . \ \

Find the limits of integration by equating -forms. \ \

and

and . \ \

Step 2: \ \

The curve is intersect the -axis at and . \ \

and .

The area of the region is \ \

\ \

square units. \ \

Solution: \ \

square units. \ \ \ \