Suppose the dimensions of your dining room are 12 feet by 14 feet. You purchase a rectangular table that is 7 feet by 9 feet. After you put the table in the dining room, how much space is left in the dining room (in square feet)?

7 x 9 = 63

12 x 14 = 274

add them together and you gey the total space left

Step-by-step explanation:

Part A. Using five rectangles.

I will use the left end-point approximation.

1. Divide the interval [0,20] into five equal subintervals

Δx = (20 - 0)/5 = 4

The intervals are:

[0,4], [4,8], [8,12], [12,16], [16,20]

2. Evaluate the function at the left end-points and calculate the areas

Fig. 1 shows the graph with five rectangles.

Part B. Using 10 rectangles

1. Divide the interval [0,20] into 10 equal subintervals

Δx = (20 - 0)/10 = 2

The intervals are:

[0,2], [2,4], [4,6], [6,8], [8,10], [10,12], [12,14], [14,16], [16,18], [18,20]

2. Evaluate the function at the left end-points and calculate the areas

Fig. 2 shows the graph with 10 rectangles.

Part C. The limit as n ⟶ ∞

Integrate the function.