Answer:
V ≅ 8980 vu
Step-by-step explanation:
According to the method of cylindrical shells V=πR²h, where R² (f(x)₂-f(x)₁), h=dx, f(x)₂=8 and f(x)₁=x³, then
V=π(8-x³)²h ⇒ dV=π(64-16x³+x⁶)dx integrating on both sides
∫dV = π∫(64-16x³+x⁶)dx = 64∫dx-16∫x³dx+∫x⁶dx ⇒
[tex]V=\pi (64x-4x^{4}+\frac{x^{7}}{7})[/tex]
[tex]V=\pi (64*5-4*5^{4}+\frac{5^{7} }{7})=\pi(320-2500+\frac{78125}{7})\\ V=\frac{\pi }{7}(2240-17500+78125)[/tex]
V ≅ 8980 vu
; evaluated to 0 ≤ x ≤ 5
