- #1
jaychay
- 58
- 0
Can you check it for me please that I have done it right or not ?
Thank you in advance.
MHB Find the volume by using shell and disk method
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The discussion focuses on verifying the calculations for finding volume using the shell and disk methods. It highlights that the integrand in the first example is reversed and provides the correct equations for the curves involved. The second example points out an incorrect curve equation, suggesting the correct form for the upper branch of the parabola. An alternative approach is proposed, translating the graphs to simplify the calculations. Overall, the thread emphasizes the importance of accurate equations and transformations in volume calculations.
Can you check it for me please that I have done it right or not ?
Thank you in advance.
- #2
skeeter
- 1,103
- 1
1st one, your integrand is reversed.
$R= 2-\cos{x}$,
$r = 2-\sqrt{4-x^2}$
2nd ... note the curve equation is incorrect.
should be $x=(y-1)^2+1 \implies y = \sqrt{x-1}+1$ for the upper branch of the parabola
alternatively, you could translate both graphs such that the parabola vertex is at the origin, $x=y^2$, with the line having the equation $y = 2-x$ and rotating the shaded region about $y=-1$
$R= 2-\cos{x}$,
$r = 2-\sqrt{4-x^2}$
2nd ... note the curve equation is incorrect.
should be $x=(y-1)^2+1 \implies y = \sqrt{x-1}+1$ for the upper branch of the parabola
alternatively, you could translate both graphs such that the parabola vertex is at the origin, $x=y^2$, with the line having the equation $y = 2-x$ and rotating the shaded region about $y=-1$
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Given:
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