A 17.7-inch-thick layer of ash and pumice has already settled onto the Forum, which is 520 feet long by 109 feet wide. What is t
2 answers:
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First of all we need to find a representation of C, so this is shown in the figure below.
So the integral we need to compute is this:
So, as shown in the figure, C = C1 + C2, so:
Computing first integral:
Applying derivative:
Substituting this value into
Computing second integral:
Applying derivative:
Substituting this differential into
We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:
![I_{2}= -8\int_{4}^{8}}dx=-8[x]\right|_4 ^{8}=-8(8-4) \rightarrow \boxed{I_{2}=-32}](https://tex.z-dn.net/?f=I_%7B2%7D%3D%20-8%5Cint_%7B4%7D%5E%7B8%7D%7Ddx%3D-8%5Bx%5D%5Cright%7C_4%20%5E%7B8%7D%3D-8%288-4%29%20%5Crightarrow%20%5Cboxed%7BI_%7B2%7D%3D-32%7D)
Finally:
So the integral we need to compute is this:
So, as shown in the figure, C = C1 + C2, so:
Computing first integral:
Applying derivative:
Substituting this value into
Computing second integral:
Applying derivative:
Substituting this differential into
We need to know the limits of our integral, so given that the variable we are using in this integral is x, then the limits are the x coordinates of the extreme points of the straight line C2, so:
Finally: