Yahoo Answers is shutting down on 4 May 2021 (Eastern Time) and the Yahoo Answers website is now in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Volume of 3-D Solid Calc Please Help!?
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=x^6,y=1,about y=10
1 Answer
- WoodsmanLv 79 years agoFavourite answer
Washer method is easiest here. Each washer has outer radius R = 10 - x^6
and inner radius r = 10 - 1 = 9, so
V = ∫[a,b] π(R²-r²) dx = π∫[-1,1] ((10 - x^6)² - 9²)dx = π∫[-1,1] (100 - 20x^6 + x^12 - 81)dx
V = π∫[-1,1] (19 - 20x^6 + x^12) dx = π(19x - (20/7)x^7 + (1/13)x^13) |[-1,1]
V = π(19 - 20/7 + 1/13 - (-19 + 20/7 - 1/13)) = (2π/91)(1729 - 260 + 7) = 2952π/91
