Question

Aflati volumul corpului obtinut prin rotatia, in jurul axei Ox a Gf.

f:[0,1], f(x)=1-x

Answer 1

$\displaystyle V = \pi\int_{0}^1f^2(x)\, dx = \pi \int_{0}^1(1-x)^2\, dx =\\ \\ =-\pi \int_{0}^1(1-x)'\cdot (1-x)^2 dx =-\pi\cdot \dfrac{(1-x)^3}{3}\Big|_{0}^1\\ \\ =-\pi\cdot \dfrac{(1-1)^3}{3}+\pi\cdot \dfrac{(1-0)^3}{3} = \boxed{\dfrac{\pi}{3}}$

Answer 2

Răspuns:

Volumul este

$\frac{\pi}{3}$