Calculate area problem given equations


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10 months ago by

Compute the area of the region enclosed by the graphs of the given equations.

y = x, y = 2x, and x = 4

add commentfollow this post modified 10 months ago by Shannon   • written 10 months ago by Jasmine  

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10 months ago by

Compute the area of the region enclosed by the graphs of the given equations. From y = x and y = 2x, we get that

x = 2x, meaning x = 0

See the following graph:

 

 Using vertical cross-sections to describe this region, we get that

 $0\le x\le4$0x4 and  $x\le y\le2x$xy2x 

So the area is

 $\int_0^4\left(Top-Bottom\right)dx=\int_0^4\left(2x-x\right)dx=\int_0^4xdx=\frac{x^2}{2}=\frac{4^2}{2}-\frac{0^2}{2}=8-0=8$04(TopBottom)dx=04(2xx)dx=04xdx=x22 =422 022 =80=8 

add comment modified 10 months ago by Shannon   • written 10 months ago by Shannon  
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