- #1
jaychay
- 58
- 0
Can you check it for me that I done it right or not ?
Thank you in advance.
Find the volume by using shell and disk method
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SUMMARY
The discussion focuses on calculating the volume of solids using the shell and disk methods in calculus. The shell method is represented by the equation $\displaystyle V = 2\pi \int_0^1 (x+2) \cdot x \, dx + 2\pi \int_1^4 (x+2) \cdot \sqrt{x} \, dx$. The disk method is illustrated with the equation $\displaystyle V = \pi \int_0^1 6^2 - (y+2)^2 \, dy + \pi \int_1^2 6^2 - (y^2+2)^2 \,dy$. Both methods are essential for finding volumes of revolution in calculus.
PREREQUISITES- Understanding of integral calculus
- Familiarity with the shell method for volume calculation
- Knowledge of the disk method for volume calculation
- Ability to evaluate definite integrals
- Study the shell method in detail with examples
- Explore the disk method and its applications
- Practice evaluating definite integrals involving polynomial and radical functions
- Learn about applications of volume calculations in real-world scenarios
Students studying calculus, educators teaching volume calculations, and anyone interested in mastering the shell and disk methods for finding volumes of solids of revolution.
Can you check it for me that I done it right or not ?
Thank you in advance.
- #2
skeeter
- 1,103
- 1
shells ...
$\displaystyle V = 2\pi \int_0^1 (x+2) \cdot x \, dx + 2\pi \int_1^4 (x+2) \cdot \sqrt{x} \, dx$
washers ...
$\displaystyle V = \pi \int_0^1 6^2 - (y+2)^2 \, dy + \pi \int_1^2 6^2 - (y^2+2)^2 \,dy$
$\displaystyle V = 2\pi \int_0^1 (x+2) \cdot x \, dx + 2\pi \int_1^4 (x+2) \cdot \sqrt{x} \, dx$
washers ...
$\displaystyle V = \pi \int_0^1 6^2 - (y+2)^2 \, dy + \pi \int_1^2 6^2 - (y^2+2)^2 \,dy$
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