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Before performing any calculation it's good to recall a few properties of integrals:


So we apply the first property in the first expression given by the question:
![\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}](https://tex.z-dn.net/?f=%5Csmall%20%5Csf%7B%5Clongrightarrow%5Cint%20%5E3_%7B-2%7D%20%5B2f%28x%29%20%2B2%5Ddx%3D%202%20%5Cint%20%5E3%20_%7B-2%7D%20f%28x%29%20dx%2B%20%5Cint%20f%5E3%20_%7B2%7D%202dx%3D18%7D)
And we solve the second integral:


Then we take the last equation and we subtract 10 from both sides:


And we divide both sides by 2:


Then we apply the second property to this integral:

Then we use the other equality in the question and we get:


We substract 8 from both sides:

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Answer:
x = 1.1
Step-by-step explanation:
x+4.6=5.7
-4.6 = -4.6
x=1.1
Okay, your answer would be 247.5mm² hope that helped