Find the area of the region between the graph of the function and the x - axis over the given interval.

Question

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

y = - 4x + 5,      [0, 1]

Answer 1

Step 1:

The function is and the interval is .

Area of the function is .

Definition of integral :

If is integrable on , then ,

Where .

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 3.

Answer 2

Contd...

Step 3:

Graph the function.

Area of the region is 3 sq-units.

Solution:

Area of the region is 3 sq-units.