More volumes revolving
- Thread starter hgaon001
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BigGlenntheHeavy
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[attachment=0:1bdpddav]aaa.jpg[/attachment:1bdpddav]
Observe the graph, the two equations intersect at (0,0) and (4,64).
The green line is f(x) = x^3 and the red line is g(x) = 4x^2.
Hence, around y axis, we have;
\(\displaystyle \pi\int_{0}^{64}[{(y^{1/3})^{2}-(\frac{\sqrt(y)}{2})^{2}]dy \ = \ \frac{512\pi}{5}, \ y=x^{3}, \ x=y^{1/3}, \ y=4x^{2}, \ x=\frac{\sqrt(y)}{2}.\)
Next one, around y = -2:
\(\displaystyle \pi\int_{0}^{4}[(4x^{2}+2)^{2}-(x^{3}+2)^{2}]dx \ = \ \frac{107,264\pi}{105}.\)
Observe the graph, the two equations intersect at (0,0) and (4,64).
The green line is f(x) = x^3 and the red line is g(x) = 4x^2.
Hence, around y axis, we have;
\(\displaystyle \pi\int_{0}^{64}[{(y^{1/3})^{2}-(\frac{\sqrt(y)}{2})^{2}]dy \ = \ \frac{512\pi}{5}, \ y=x^{3}, \ x=y^{1/3}, \ y=4x^{2}, \ x=\frac{\sqrt(y)}{2}.\)
Next one, around y = -2:
\(\displaystyle \pi\int_{0}^{4}[(4x^{2}+2)^{2}-(x^{3}+2)^{2}]dx \ = \ \frac{107,264\pi}{105}.\)
