Engineering, 09.12.2019 02:31 clashofclans17
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.
y = 5x2, y = 30x − 10x2
Answers: 1
![= \int^{2}_{0}\ 2 \pi x (30x - 10x^2 - 5x^2) \ dx\\\\= 2 \pi \int^{2}_{0} x (30x - 15x^2) \ dx\\\\= 30 \pi \int^{2}_{0} (2x^2 - x^3) dx\\\\= 30 \pi ( \frac{2x^3}{3} - \frac{x^4}{4})^{2}_{0}) \\\\= 30 \pi ( \frac{2(2)^3}{3} - \frac{(2)^4}{4}-0)] \\\\= 30 \pi [( \frac{2 \times 8}{3} - \frac{16}{4}-0] \\\\= 30 \pi [( \frac{16}{3} - \frac{16}{4}] \\\\= 30 \pi [( \frac{64-48}{12} - 4] \\\\= 30 \pi [( \frac{16}{12})] \\\\= 30 \pi [( \frac{4}{3})] \\\\= 30 \pi \times \frac{4}{3} \\\\= 40 \pi](/tpl/images/0409/4565/92f07.png)
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by...
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