Question

Consider the following. y = x2 y = 20 − x Maple Generated Plot (a) Find the area of the region by integrating with respect to x.onsider the following. y = x2 y = 20 − x Maple Generated Plot (a) Find the area of the region by integrating with respect to x.

Answer 1

Answer:

  area = 121.5

Step-by-step explanation:

See below for a plot and the integral. We assume you are interested in the entire bounded region.

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  $\displaystyle\text{area}=\int_{-5}^4{(20-x-x^2)}\,dx=\left.20x-\dfrac{x^2}{2}-\dfrac{x^3}{3}\right|_{-5}^4\\\\=20(4-(-5))-\dfrac{4^2-(-5)^2}{2}-\dfrac{4^3-(-5)^3}{3}\\\\=180+\dfrac{9}{2}-63=121.5$