I just started Calculus 2 recently and while things were running smoothly, I am having trouble with volumes.
At first I tried with this question the Vertical Revolution formula:
2π 0to6 (bounds) (5sqrtx)(6)dx, multiplying and integrating for 20x^3/2 and plugging in 6, since 0 is 0, but then I got 293.9387, which wasn't right.
I appreciate any help, and I can provide any more information if needed, thank you. Sorry if the formatting is off.
Given that : $$y=5\sqrt{x}$$ $$y^2=25x$$ $$\frac{y^2}{25}=x$$ $$x=\frac{y^2}{25}$$ $$f(y)=\frac{y^2}{25}$$
Use the formula : $$V=\pi \int _a^b\left(f\left(y\right)\right)^2\:dy$$ $$V=\pi \int _0^6\left(\frac{y^2}{25}\right)^2\:dy\:$$ $$V=\pi \int _0^6\left(\frac{y^4}{625}\right)\:dy\:$$ $$V=\pi \left[\frac{y^5}{3125}\right]_{0\:}^6$$ $$V=\frac{7776\pi }{3125}$$