Question #315199

Find the volume generated if the region enclosed by y = x² and the line y = 2x is revolve about the x-axis. Answer in 2 decimal places.



1
Expert's answer
2022-03-21T09:21:23-0400

y=x2,y=2x.y=x^2, y=2x.\\

x22x=0,x(x2)=0,x1=0,x2=2.V=π02(4x2x4)dx==π(43x315x5)02==π(43231525)==π(323325)==32π(1315)==64π15=13.40x^2-2x=0, x(x-2)=0,\\ x_1=0, x_2=2.\\ V=\pi \int^2_0 (4x^2-x^4)dx=\\ =\pi(\frac{4}{3}x^3-\frac{1}{5}x^5)|^2_0=\\ =\pi(\frac{4}{3}2^3-\frac{1}{5}2^5)=\\ =\pi(\frac{32}{3}-\frac{32}{5})=\\ =32\pi(\frac{1}{3}-\frac{1}{5})=\\ =\frac{64\pi}{15}=13.40


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