You must be logged in to see worked solutions.

Already have an account? Log in here.

Integration extends to the third dimension with the means to compute the volumes of shapes obtained by revolving regions around an axis, such as spheres, toroids, and paraboloids.

The above diagram shows the points \(R=(7,\frac{1}{7})\) and \(P=(14,\frac{1}{14}),\) which lie on the curve \(y=\frac{1}{x},\) point \(Q = (0, \frac{1}{7}) \) on the \(y\)-axis, and points \(A = (7,0)\) and \(B = (14,0)\) on the \(x\)-axis. If \(S\) is the solid obtained by rotating the region \(R\) bounded by \[\overline{OQ}, \overline{QR}, \widehat{RP}, \overline{PB}, \text{ and } \overline{OB}\] about the axis of rotation \(x=-7\) and the volume of \(S\) is \(\alpha \pi, \) what is \(\alpha?\)

**Note:** The above diagram is not drawn to scale.

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

You must be logged in to see worked solutions.

Already have an account? Log in here.

×

Problem Loading...

Note Loading...

Set Loading...