Area inside the curve and the line x=0

Question

Find the area between the curve with equation $x+2|y|=1$ and the line $x=0$(y axis)

Answer 1

First graph both curves:

Then notice that these curves can be expressed as functions of $y$ but not functions of $x$. So we write the two curves as $x=1-2|y|$ and $x=0$. Then we integrate the difference of the two, so that we get the area between them, with respect to $y$:

$$\begin{align}\int_{-1/2}^{1/2} \big[(1-2|y|)-(0)\big]\ dy &= \int_{-1/2}^{1/2} \big(1-2|y|\big)\ dy \\ &= \int_0^{1/2} (1-2y)\ dy + \int_{-1/2}^{0} \big(1-2(-y)\big)\ dy\end{align}$$

This should be pretty easy to integrate.

Answer 2

See that the best thing is to draw the graph of that equation see that you will get a triangle and you can calculate the area.

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