Answer to Question #129481 in Calculus for Jade

Question #129481
Find the volume of the solid generated by rotating the region bounded by the curves y=0, y=x^2+x, and x=2 about the y-axis
1
Expert's answer
2020-08-19T15:02:48-0400



"V = \\int_{0}^{2} 2\\pi x*(x^2 +x) dx ="


"= 2\\pi \\int_{0}^{2} x^3 +x^2 dx = 2\\pi [\\frac{x^4}{4} + \\frac{x^3}{3}] \\Big\\vert_{0}^{2} ="


"= 2\\pi [4+ \\frac{8}{3}] = 2\\pi [\\frac{20}{3}] = \\frac{40 \\pi}{3}"

Answer

"V = \\frac{40\\pi}{3}"



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