Mathematics, 14.07.2019 09:00 Lizzy527663
The region in the first quadrant bounded above by the line yequals=77, below by the curve yequals=startroot 7 x endroot7x, and on the left by the y-axis is revolved about the line yequals=77. find the volume of the resulting solid.
Answers: 1
![V=\displaystyle \int_{0}^{7}{\pi\left(7-\sqrt{7x}\right)^{2}\,dx}\\\\=\pi\left[49x-\dfrac{28x\sqrt{7x}}{3}+\dfrac{7x^2}{2}\right]\limits_{0}^{7}\\\\=49\pi\left(7-\dfrac{28}{3}+\dfrac{7}{2}\right)\\\\V=343\cdot \dfrac{\pi}{6}\approx 179.59438](/tpl/images/0088/0900/e8e16.png)
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