Question

Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x - axis over the given interval.

f (x) = 2x + 5,  [0, 2], 4 rectangles

Answer 1

Step 1:

The function is , interval is .

Number of rectangles is .

The sum of all inscribed rectangle is Lower sum.

where

The sum of all circumscribed rectangle is Upper sum.

.

where

Where .

Step 2:

Lower Sum:

Area of lower sum is

Sum of natural numbers is .

Step 3:

Upper Sum:

Area of higher sum is

Sum of natural numbers is .

Then

Solution :

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