I NEED THIS ASAP In this task, you will practice finding the area under a nonlinear function by using rectangles. You will use graphing skills in addition to the knowledge gathered in this unit. Sketch the graph of the function y = 20x − x2, and approximate the area under the curve in the interval [0, 20] by dividing the area into the given numbers of rectangles. Part A Use five rectangles to approximate the area under the curve. Part B Use 10 rectangles to approximate the area under the curve. Part C Calculate the area under the curve using rectangles as their number becomes arbitrarily large (tends to infinity). You do not need to sketch the rectangles.

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.

step-by-step explanation:

for the free