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Numerade Educator

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Problem 42 Easy Difficulty

Each integral represents the volume of a solid. Describe the solid.

$ \pi \displaystyle \int_{1}^4 [3^2 - (3 - \sqrt{x})^2] dx $

Answer

The solid is obtained by rotating the region bounded by $y=3-\sqrt{x}$ and
$y=3$ in the interval $[1,4]$ about $x$ -axis

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Video Transcript

We know that when we're looking integration with respect to X, we know rotation is about the X axis, not the y axis. Therefore, we know we have an outer and inner radius out of radius is three and a radius is three mine escort of acts. Therefore, we know we obtained this by rotating the region around. Why is three months skirt of X and why is three in the interval 14 about the X axis?