User:Sunjay

Hello, my name is Sunjay. Not Sunjay or Sunjoy or Sanjaya. It's Sunjay.

${\frac {1}{3}}\int _{a}^{b}r(\theta )^{2}h(\theta )\,d\theta$

$3\cdot {\frac {1}{2}}\int _{0}^{2\pi }r(\theta )^{2}\,d\theta \,\approx \,805.8185ft^{3}$

${\frac {1}{3}}\cdot {\frac {1}{4}}\int _{-{\frac {\pi }{6}}}^{\frac {\pi }{2}}r(\theta )^{3}\,d\theta \,\approx \,148.4403ft^{3}$

${\frac {1}{3}}\cdot {\frac {1}{3}}\int _{\frac {\pi }{2}}^{\frac {7\pi }{6}}r(\theta )^{3}\,d\theta \,\approx \,197.9203ft^{3}$

${\frac {1}{3}}\cdot {\frac {1}{2}}\int _{\frac {7\pi }{6}}^{\frac {11\pi }{6}}r(\theta )^{3}\,d\theta \,\approx \,296.8805ft^{3}$

$\int _{0}^{2\pi }{\sqrt {r^{2}+\left({\frac {dr}{d\theta }}\right)^{2}}}\,d\theta$

$\int _{-{\frac {\pi }{6}}}^{\frac {\pi }{2}}\left({\frac {r(\theta )}{4}}+3\right){\sqrt {r^{2}+\left({\frac {dr}{d\theta }}\right)^{2}}}\,d\theta \,\approx \,122.8734ft^{2}$

$\int _{\frac {\pi }{2}}^{\frac {7\pi }{6}}\left({\frac {r(\theta )}{3}}+3\right){\sqrt {r^{2}+\left({\frac {dr}{d\theta }}\right)^{2}}}\,d\theta \,\approx \,140.8319ft^{2}$

$\int _{\frac {7\pi }{6}}^{\frac {11\pi }{6}}\left({\frac {r(\theta )}{2}}+3\right){\sqrt {r^{2}+\left({\frac {dr}{d\theta }}\right)^{2}}}\,d\theta \,\approx \,176.7490ft^{2}$

${\frac {1}{2}}\int _{0}^{2\pi }r(\theta )^{2}\,d\theta \,\approx \,268.6062ft^{3}$