Mathematics, 07.08.2021 17:20 levicorey846
HELPP Sketch the graph of the function y = 20x β 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.
Answers: 3
![\displaystyle \sum_{i=1}^{n} i= \dfrac{n*(n+1)}{2} \\\\\displaystyle \sum_{i=1}^{n} i^2= \dfrac{n*(n+1)(2n+1)}{6} \\\\\\\int\limits^{20}_0 {(20\ x-x^2)} \, dx =[\dfrac{20\ x^2}{2} -\dfrac{x^3}{3} ]^{20}_0=\dfrac{20^3}{3} =1333.\overline{3}\\\\\\](/tpl/images/1405/7335/9341f.png)
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HELPP Sketch the graph of the function y = 20x β x2, and approximate the area under the curve in the...
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