Question

vol corpului obtinut prin rotatia subgraf functiei definite pe [0,3],unde f este x[x-3] /[x-4] toat afractia fiind sub radical

Answer 1

Răspuns:

Explicație pas cu pas:

$\displaystyle V=\pi\cdot\int_0^3\left(\sqrt{\dfrac{x(x-3)}{(x-4)}}\right)^2dx=\pi\cdot\int_0^3\dfrac{x(x-3)}{x-4}dx=\pi\cdot\int_0^3\dfrac{x^2-3x}{x-4}=\\=\pi\cdot\int_0^3\dfrac{x^2-4x+x-4+4}{x-4}dx=\\=\pi\left(\cdot\int_0^3\dfrac{x^2-4x}{x-4}dx+\int_0^3\dfrac{x-4}{x-4}dx+4\int_0^3\dfrac{1}{x-4}\right)dx=\\=\pi\cdot\left(\int_0^3xdx+\int_0^3dx+4\ln|x-4|~|_0^3\right)=\\=\pi\cdot\left(\dfrac{x^2}{2}|_0^3+x|_0^3+4\ln 1-4\ln4\right)=\pi\cdot\left(\dfrac{9}{2}+3-4\ln4\right)$