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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

I will calculate \(\displaystyle V_x\) and \(\displaystyle V_y\) I start to get crit point \(\displaystyle x_1=0\) and \(\displaystyle x_2=7\)

rotate on y-axe:

\(\displaystyle 2\pi\int_a^bf(x)dx\)

so we get \(\displaystyle 2\pi[\frac{7x^2}{2}-\frac{x^3}{3}]_0^7\) \(\displaystyle V_y=\frac{2\pi*343}{6}\)

rotate on x axe:

\(\displaystyle \pi\int_a^bf(x)^2dx\)

so we start with:\(\displaystyle (7x-x^2)^2=49x^2-14x^3+x^4\) so we get \(\displaystyle [\frac{49x^3}{3}-\frac{14x^4}{4}+\frac{x^5}{5}]_0^7\) that means \(\displaystyle V_x=\frac{16087\pi}{30}\) What I am doing wrong?

(Sorry for bad english.)