Question 1 (7 points)
Find the volume of the solid generated by revolving the region bounded by the graphs of $y = 0, x = 2$ , and $y = x^{2}$ about the line $y = 5$
Show all your steps in your partial credit submission.
(Round your answer to three decimal places as necessary.)
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$V = π {[\frac{1}{5} x^{5} - \frac{10}{3} x^{3} + 25 x]}_{0}^{2}$

Steps

Step 1 ： $V = π \int_{0}^{2} (5 - x^{2})^{2} - (5)^{2} d x$

Step 2 ： $V = π \int_{0}^{2} (25 - 10 x^{2} + x^{4}) - 25 d x$

Step 3 ： $V = π {[\frac{1}{5} x^{5} - \frac{10}{3} x^{3} + 25 x]}_{0}^{2}$