I have to find the area between the curves $x^2=y^3$ and $x=y$. How do I plot the curve $x^2=y^3$?. I have no experience if working with such curves. The only thing i have been able to do till now is find the intersection points $(0,0)$ and $(1,1)$
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Please help guys . I have no idea of how to plot that curve – joey lang Sep 24 '17 at 15:27
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You can always use Desmos. – Jens Sep 24 '17 at 15:58
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thanks for the suggestion . i asked this question as i wanted to know about the nature of the curve and what this curve is called. and how to plot it if i get it in my exam? – joey lang Sep 24 '17 at 16:02
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Taking the cuberoot on each side you get $y=x^{\frac {2}{3}}$. – Jens Sep 24 '17 at 16:08
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is y=x^(2/3) a parabola? – joey lang Sep 24 '17 at 16:10
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Note that the LHS is non-negative so $y \geq 0$. Also note that if you replace $x$ with $x$, then the $y$ value doesn't change, so this graph is even (reflective over $y$-axis). Thus, if you graph $y=x^{\frac{2}{3}}$ and reflect over the $y$-axis, you get your plot of $x^2=y^3$. Use Desmos or Geogebra (both online graphing calculators) if you don't know how to graph this.
Sharky Kesa
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