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How to calculate these exercises in wolfram

Hi guys, I want you to help me please as finding areas between curves and calculation of areas. Here's an exercise to chart, and not as it is in Wolfram.

Calculate the area of the region bounded by the graphs of equations 2y ^ 2 = x + 4 and x = y ^ 2

2 Replies

Hi David,

I am not sure whether I fully understand your question, but this might help. First we can plot the curves>

ContourPlot[{2 y^2 == x + 4, x == y^2}, {x, -4, 10}, {y, -4, 4}]

which gives

enter image description here

Now you see that the area between the curves will be infinite, because there is a difference of the curves right of the intersection points. For the next calculation I assume that you want the area of the finite bit for $-4<x<4$. In that case you could try

Integrate[2*Sqrt[(x + 4)/2], {x, -4, 0}] + Integrate[2*(Sqrt[(x + 4)/2] - Sqrt[x]), {x, 0, 4}]

Which gives, after using Simplify, 32/3. Alternatively, this should work

Integrate[x^2 - (2 x^2 - 4), {x, -2, 2}]

Luckily, it gives the same result.

Cheers,

Marco

POSTED BY: Marco Thiel
In[2]:= Integrate[
 Boole[2 y^2 <= x + 4 && 
   x <= y^2], {x, -\[Infinity], \[Infinity]}, {y, -\[Infinity], \
\[Infinity]}]

Out[2]= 32/3
POSTED BY: Frank Kampas
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