In this problem, I am trying to find the volume of the solid gotten by rotating the shaded area around the x-axis. The equation of a circle is $x^2+y^2=r^2$. If I am integrating using the shell method, I know the height and radius that I need (height = $\sqrt{r^2-y^2}$ and radius = y). My upper limit of integration is r. My lower limit of integration is c. I also see that when making a right triangle, c is opposite my hypotenuse which - so maybe I can use the sine function?

How should I figure out how to put c in terms of r?

  • $\begingroup$ Yes, $\frac12=\sin{30^\circ}=\frac{c}{r}$ $\endgroup$ – saulspatz Dec 20 '19 at 16:13

Yes you are right, you should continue by using the trigonometric sine function. Which leads to $c = r.Sin(\theta)$

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