Calculating Area Using Integrals for Complex Building Shapes

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The discussion focuses on calculating the area of complex building shapes using integrals, specifically through the integration of two functions. The integrals presented are from -5.5 to 0 of (1/3)√(5+x)dx and from 0 to 5.5 of (1/3)√(5-x)dx. The user encountered an issue when evaluating the first integral, resulting in the square root of a negative number, indicating a potential mistake in the setup of the integral limits or functions. Ultimately, the user resolved the issue independently.

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concrete sections for a new building have the dimensions in meters and shapw shown in the figure.

a)find the area of the face of the section superimposed on the rectangular coordinate system.


The way i tried to solve this was to split it up into 2 integrals and add them together to get the area

the integrals were

integral from -5.5 to 0 of 1/3*sqrt(5+x)dx + integral from 0 to 5.5 of 1/3*sqrt(5-x)dx

I tried the first part and got

2/9*(5+x)^(3/2) but when you evaluate it at -5.5 you end up taking the squareroot of a negative number.

Did i do it completely wrong? or did i just make a simple mistake?

any help would be appreciated.
 

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figured it out, couldn't figure out how to delete a post though.
 

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