(a) If the region shown in the figure is rotated about the x-axis to form a solid, use the Midpoint Rule with $ n = 4 $ to estimate the volume of the solid.

(b) Estimate the volume if the region is rotated about the y-axis. Again use the Midpoint Rule with $ n = 4 $.

a) 196 units $^{3}$

b) 838 units $^{3}$

Applications of Integration

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Okay. The first step to use them in point formula would be to calculate Delta X or the change in ax by using the Formula B minus over and we plug in 10 minutes to over four witches, too, transitioning over into putting into volume. We know we take the Delta Axe, which is two times pi times off of three squared, plus a five squared plus up of seven squared puts off of nine squared, which gives us two pi times 31.14 which is 196 units cubed. Now we're looking at part B. Do the same thing built axe. You might stay over on. Now we end up with one. We're doing the same thing playing the same formula. Delta X times Pie times outer squared, my inner squared plus outer squared minus inter squared, which gives 838 units. Cute