Final answer to the problem
$\frac{-179685\cdot -\pi }{16}+131.3333333+\frac{179685\pi }{16}+\frac{-0.3333333\cdot -\pi }{4}+\frac{0.3333333\pi }{4}$
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Step-by-step Solution
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- Integrate by partial fractions
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1
Simplify the expression
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$\int_{0}^{66}\frac{x^2\sqrt{66x-x^2}}{33}dx+\int_{0}^{66}\frac{\sqrt{66x-x^2}}{99}dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (x^2)/33(66x-x^2)^(1/2)+((66x-x^2)^(1/2))/99 from 0 to 66. Simplify the expression. The integral \int_{0}^{66}\frac{x^2\sqrt{66x-x^2}}{33}dx results in: \frac{1}{33}\int_{0}^{66} x^2\sqrt{66x-x^2}dx. The integral \int_{0}^{66}\frac{\sqrt{66x-x^2}}{99}dx results in: \frac{1}{99}\int_{0}^{66}\sqrt{66x-x^2}dx. Gather the results of all integrals.
Final answer to the problem
$\frac{-179685\cdot -\pi }{16}+131.3333333+\frac{179685\pi }{16}+\frac{-0.3333333\cdot -\pi }{4}+\frac{0.3333333\pi }{4}$
