0 ≤ x ≤ 3
[m]V_{Ox}=π ∫ ^{3}_{0}(2x)^2dx=8π ∫ ^{3}_{0}x^2dx=8π (\frac{x^3}{3})|^{3}_{0}=\frac{8}{3}π\cdot 3^3=72π[/m]
2)
2)y=x^3, 1<x<2.
[m]V_{Ox}=π ∫ ^{2}_{1}(x^3)^2dx=π ∫ ^{2}_{1}x^6dx=π (\frac{x^7}{7})|^{2}_{1}=\frac{1}{7}\cdot π\cdot (2^7-1^7)=\frac{127}{7}π[/m]
3)y=x^2, 2<x<4.
[m]V_{Ox}=π ∫ ^{4}_{2}(x^2)^2dx=π ∫ ^{4}_{2}x^4dx=π (\frac{x^5}{5})|^{4}_{2}=\frac{1}{5}\cdot π\cdot (4^5-2^5)=\frac{256-32}{5}π[/m]
4)y=√x, 0<x<4
[m]V_{Ox}=π ∫ ^{4}_{0}(√x)^2dx=π ∫ ^{4}_{0}xdx=π (\frac{x^2}{2})|^{4}_{0}=\frac{1}{2}\cdot π\cdot (4^2-0^2)=8π[/m]