Mathematics: Find the area that is enclosed by the parabola y = x²-3x line y = 2x and line y = -x

3 miles per hour.Step-by-step explanation:...

Find the area that is enclosed by the parabola y =

Ответ:

lilyclairehutson

24.01.2021

Mathematics

39/2

Step-by-step explanation:

First, we find the points of intersection (POI) of the curve and one of the lines:

x²-3x=2x

x²-5x=0

x(x-5)=0

x=0,5

Next, we find the POI of the curve and the second line:

x²-3x=-x

x²-2x=0

x(x-2)=0

x=0,2

To better visualize this, you can go on Desmos.

The area enclosed by all three lines is going to be the area enclosed by the curve and y=-x ( $S_{2}$ ) subtracted from the area enclosed by the curve and y=2x ( $S_{1}$ ).

Since 2x is greater than the curve in the interval [0,5],

$S_{1}$ = $\int _0^5\:(2x-(x^{2}-3x))dx$

Solving this, you would get 125/6.

Since -x is greater than the curve in the interval [0,2],

$S_{2}$ = $\int _0^2\:(-x-(x^{2}-3x))dx$

Solving this, you would get 4/3.

$S_{1}-S_{2}$ =125/6-4/3=39/2

Hope this helps!

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Find the area that is enclosed by the parabola y = x²-3x line y = 2x and line y = -x

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