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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\(V = \pi \left[ \dfrac{1}{5}x^5 - \dfrac{10}{3}x^3 + 25x \right]_{0}^{2}\)

Steps

Step 1 ：\(V = \pi \int_0^2 (5-x^2)^2 - (5)^2 dx\)

Step 2 ：\(V = \pi \int_0^2 (25 -10x^2 + x^4) - 25 dx\)

Step 3 ：\(V = \pi \left[ \dfrac{1}{5}x^5 - \dfrac{10}{3}x^3 + 25x \right]_{0}^{2}\)