Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = (7x + 6)^(-1/2) y = 0 x = 0 x = 4

V = .779 (that's with pi multiplied in)

Step-by-step explanation:

We will use the disk method here with a vertical representative rectangle.  With this method, we use y = x equations and x intervals.  The height of the rectangle is the curve itself, and since there is no space between the solid and the axis of revolution, the integral looks like this:

When you square a square root it's eliminated, so we simply have:

Now we integrate.  This pattern follows that of the natural log.  Identify the "u" we need and take it from there.

u = 7x + 6

du = 7 dx and, finally,

. Our integral is as follows:

[ln(7x+6)] from 0 to 4.

Filling in our bounds applying the First Fundamental Theorem of Calculus:

[3.526360525 - 1.791759469] and

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