Question

Use the midpoint rule

with n = 4 to approximate the area of the region bounded by the graph of the function and the x - axis over the given interval.

f (x) = x^2 + 3,    [0, 2]

Answer 1

Step 1:

The integral expression is  on interval .

 The expression is .

Consider .

Using summation theorem :

If is integral on , then .

Where , and .

The integral expression is .

Step 2:

Here and .

Substitute  in .

.

.

Step 3:

substitute values from 1 to 4.

Step 4:

 using mid point theorem:

Area =.

.

Solution:

Area of the function is .