Use limit process to find area bounded by graph

Question

Use the limit process to find the area of the region bounded by the graph of the function and the x- axis over the given interval y=4-x^2 [-2,2]

Answer 1

Step 1:

The function is  and the interval is .

Area of the function is .

Where and .

Let number of subintervals be .

Substitute  in .

.

Step 2:

Find the area of the region bounded by the function with -axis.

Apply summation formula .

Apply summation formula .

As , then .

Area of the region is between and -axis is .

Solution:

Area of the region is between and -axis is .