Exercise
$\int_0^{66}\left(\frac{x^2}{33}\sqrt{66x-x^2}+\frac{\sqrt{66x-x^2}}{99}\right)dx$
Step-by-step Solution
Final answer to the exercise
$\frac{-35937\cdot -33\cdot 2\sqrt{- 1089+1089}}{4356}-\frac{35937}{2}\cdot \left(-\frac{\pi }{2}\right)+\frac{35937\cdot 33\cdot 2\sqrt{- 1089+1089}}{4356}+\frac{35937}{2}\cdot \frac{\pi }{2}-\frac{5}{3}+\frac{107811\cdot -33\cdot 2\sqrt{- 1089+1089}}{17424}+\frac{107811\cdot -\pi }{8\cdot 2}+\frac{33-\frac{1}{33}\sqrt{\left(- 1089+1089\right)^{3}}}{4}+\frac{-107811\cdot 33\cdot 2\sqrt{- 1089+1089}}{17424}+\frac{-107811\pi }{8\cdot 2}+\frac{33-\frac{1}{33}\sqrt{\left(- 1089+1089\right)^{3}}}{4}+\frac{-35937\cdot -33\cdot 2\sqrt{- 1089+1089}}{4356}+\frac{-35937\cdot -\pi }{2\cdot 2}+\frac{1185921\cdot 2\sqrt{- 1089+1089}}{4356}+\frac{35937\pi }{2\cdot 2}+\left(\frac{1}{2}\cdot \left(-\frac{\pi }{2}\right)-33\left(\frac{1}{2178}\right)\sqrt{- 1089+1089}\right)-\frac{1}{3}+\left(\frac{1}{2}\cdot \frac{\pi }{2}+33\left(\frac{1}{2178}\right)\sqrt{- 1089+1089}\right)\frac{1}{3}$