A curve is specified as y = sqrt{frac{4x}{x^2 + 6}}. The region of the xy-plane enclosed by this curve and the x-axis between x = 1 and x = 2 is rotated about the x-axis through 2pi radians. Find the volume of the resulting solid.
Added by Francisco O.
Step 1
When y = 0, we have: 0 = \sqrt{\frac{4x}{x^2 + 6}} Squaring both sides, we get: 0 = \frac{4x}{x^2 + 6} 0 = 4x x = 0 So, the curve intersects the x-axis at x = 0. Show more…
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$\begin{array}{l}{\text { The region under the curve } y=\sin ^{2} x \text { from } 0 \text { to } \pi \text { is rotated }} \\ {\text { about the } x \text { -axis. Find the volume of the resulting solid. }}\end{array}$
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