find the area of the region between the graph of the function and the y - axis over the given y - interval.

Question

Use the limit process to find the area of the region between the graph of the function and the y - axis over the given y - interval. Sketch the region.

f (y) = 4y, 0 ≤ y ≤ 2

Answer 1

Step 1:

The function is and .

Area of the region is .

Definition of integral :

If is integrable on , then ,

Where and .

Let number of sub intervals be

Substitute  in .

Step 2:

Sum of first natural numbers is .

Area of the region is between and -axis is 8.

Answer 2

Contd....

Step 3:

Graph the function.

Area of the region is 8 sq-units.

Solution:

Area of the region is 8 sq-units.