help-area-curves?

Question

Answer 1

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:

Graph the region:

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:.

Comments

Contd..

square units.

Solution:

square units.

Answer 2

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.

and

and .

Step 2:

The curve is intersect the -axis at .

The area of the region is .

square units.

Solution:

square units.