### Calculate area problem given equations

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

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

Community: Demo Calculus Class

### 1 Answer

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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$0≤`x`≤4 and $x\le y\le2x$`x`≤`y`≤2`x`

So the area is

$\int_0^4\left(Top-Bottom\right)dx=\int_0^4\left(2x-x\right)dx=\int_0^4xdx=\frac{x^2}{2}=\frac{4^2}{2}-\frac{0^2}{2}=8-0=8$∫_{0}^{4}(`T``o``p`−`B``o``t``t``o``m`)`d``x`=∫_{0}^{4}(2`x`−`x`)`d``x`=∫_{0}^{4}`x``d``x`=`x`^{2}2 =4^{2}2 −0^{2}2 =8−0=8

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