Find the volume about the x-axis

[js009]

Hello, I am having difficulties with the following problem. As my results do not seem to be correct.
the functions are Y= 13/7 - X^2 and Y= 6/7X^2. I have the graphs completed. My calculations though are wrong. Here is what the work I did. Although I know it's not right.

piR-pir=pi(R-r)
=pi[(13/7-X^2)^2-(6/7X^2)^2]
=2pi integral (from 0 lower limit to 1 upper limit) 169/49-26/7X^2+X^4-36/49X^4
F(x)=169/49X-26/21X^3+13/245X^5
2pi[169/49X-26/21X^3+13/245X^5] (from 0 lower limit to 1 upper limit)
=2pi[338/49-208/21+416/245-0]
=2pi[-442/147+416/245]
=2pi[-442/147+416/245]
=2pi[-962/735]
=-1924/735 pi

 

[stapel]

Hello, I am having difficulties with the following problem. As my results do not seem to be correct.
the functions are Y= 13/7 - X^2 and Y= 6/7X^2. I have the graphs completed. My calculations though are wrong. Here is what the work I did. Although I know it's not right.

piR-pir=pi(R-r)
=pi[(13/7-X^2)^2-(6/7X^2)^2]
=2pi integral (from 0 lower limit to 1 upper limit) 169/49-26/7X^2+X^4-36/49X^4
F(x)=169/49X-26/21X^3+13/245X^5
2pi[169/49X-26/21X^3+13/245X^5] (from 0 lower limit to 1 upper limit)
=2pi[338/49-208/21+416/245-0]
=2pi[-442/147+416/245]
=2pi[-442/147+416/245]
=2pi[-962/735]
=-1924/735 pi

From the highlighted portions of the following two lines:

. . . . .=2pi integral (from 0 lower limit to 1 upper limit) 169/49-26/7X^2+X^4-36/49X^4
. . . . .F(x)=169/49X-26/21X^3+13/245X^5

...it appears that, by "169/49x", you actually mean "(169/49)x". In other words, where you write:

. . . . .\(\displaystyle \dfrac{169}{49x}\)

...you mean:

. . . . .\(\displaystyle \dfrac{169}{49}x\)

Is this correct? Thank you.

 

[Ishuda]

Hello, I am having difficulties with the following problem. As my results do not seem to be correct.
the functions are Y= 13/7 - X^2 and Y= 6/7X^2. I have the graphs completed. My calculations though are wrong. Here is what the work I did. Although I know it's not right.

piR-pir=pi(R-r)
=pi[(13/7-X^2)^2-(6/7X^2)^2]
=2pi integral (from 0 lower limit to 1 upper limit) 169/49-26/7X^2+X^4-36/49X^4 <=====(1)
F(x)=169/49X-26/21X^3+13/245X^5
2pi[169/49X-26/21X^3+13/245X^5] (from 0 lower limit to 1 upper limit)
=2pi[338/49-208/21+416/245-0] <=====(2)
=2pi[-442/147+416/245]
=2pi[-442/147+416/245]
=2pi[-962/735]
=-1924/735 pi

A small typo(?)
piR²-pir²=pi(R²-r²)

See above
(1) Why the 2pi now instead of just pi?
(2) You went astray at this point, for example
\(\displaystyle -\frac{26}{21}x^3|_0^1\, = -\frac{26}{21}(1\, -\, 0)\, = -\frac{26}{21}\)