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(a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.

(b) Use your calculator to evaluate the integral correct to five decimal places.

$ x^2 - y^2 = 7 $ , $ x = 4 $ ; about $ y = 5 $

a) $V=2 \pi \int_{-3}^{3}(5-y)\left(4-\sqrt{7+y^{2}}\right) d y$

b) $\approx 163.02712$

Applications of Integration

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okay, we know we have excess scored of seven plus y squared and exes for. So what we're gonna do is we're gonna set these equal to each other and then solve seven plus y squared. So for why, why is plus or minus three? These are to bounce negative and positive three per a plug into the formula for volume two pride times the integral from our bounds again. Negative three deposited. Three are two bounds. And now we're gonna be multiply our times h which means we have five minus. Why this the given region? We are we rooting about the region five and we know that we have five minutes Why of r and then we have a TSH four minus squirt of seven plus y squared. This came from above over here when we were setting this equal to zero. Okay, this was part a was driving the integral and writing it out. Now for part B, we can simply use the calculator, plug it into graphing calculator, math way, any sort of calculator to solve and you get 1 63 and then we have to write out the decimal places 0.2712 as our solution