Mathematics: 100 points if right troll answers get reported

100 points if right troll answers get reported

Ответ:

mjam85877

30.11.2021

Mathematics

$\large \boxed{\text{Part A. 1280; Part B. 1320; Part C; 1333}}$

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

$\begin{array}{rrr}\mathbf{x} & \mathbf{f (x)}&\textbf{Area} \\0 &0&0 \\4 & 64&256 \\8 & 96&384 \\12 & 96&384 \\16 & 64&256 \\&\textbf{TOTAL =}& \mathbf{1280}\end{array}\\\text{The area of five rectangles is $\large \boxed{\mathbf{1280}}$}$

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

$\begin{array}{rrr}\mathbf{x} & \mathbf{f (x)}&\textbf{Area} \\0 &0&0 \\2 & 36&72 \\4 & 64&128 \\6 & 84&168 \\8 & 96&192 \\10 &100&200 \\12 & 96&192 \\14 &84&168 \\16 & 64&128 \\18 &36&72 \\&\textbf{TOTAL =}& \mathbf{1320}\end{array}\\\text{The area of 10 rectangles is $\large \boxed{\mathbf{1320}}$}$

Fig. 2 shows the graph with 10 rectangles.

Part C. The limit as n ⟶ ∞

$\displaystyle \lim_{n\longrightarrow \,\infty} \sum_{i = 1}^{n} f(x_{i-1})\Delta x= \int_{a}^{b}f(x)dx$

Integrate the function.

$\displaystyle \int_{0}^{20}(20x-x^{2})dx= \left[10x^{2}- \dfrac{1}{3}x^{3}\right]_{0}^{20} =4000 - \dfrac{8000}{3} = \dfrac{12000 - 8000 }{3}\\\\ = \dfrac{4000}{3} \approx\mathbf{1333}$

I NEED THIS ASAP In this task, you will practice finding the area under a nonlinear function by usin

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