help? area? [curves]?

Question

Answer 1

(3)

Step 1 :

The curve equation is and a line equation .

Sketch the graphs :

Shade the region above the curve and region below the line .

Now find the intersection of the curve and a line.

Find the intersection points from the graph:

The intersection points are and .

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

.

Here integral limits are and .

Apply power rule of integration: .

Therefore area above the curve and region below the line is 36 sq units.

Solution:

Area above the curve and region below the line is 36 sq units.

Answer 2

(4)

Step 1 :

The curve equation is and a line equation .

Sketch the graphs :

Shade the left side region of the curve and right side region of the line .

Now find the intersection of the curve and a line.

Find the intersection points from the graph and .

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

.

Here integral limits are and .

Apply power rule of integration: .

Therefore, the area of the intersection region is 24.67 sq units.

Solution:

Area is 24.67 sq units.