- #1
jaychay
- 58
- 0
Can you check it for me that I 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 volume using both the shell and disk methods. For the shell method, the volume is calculated as V = 2π ∫ from 0 to 1 of (x+2)·x dx plus 2π ∫ from 1 to 4 of (x+2)·√x dx. For the disk method, the volume is expressed as V = π ∫ from 0 to 1 of (6^2 - (y+2)^2) dy plus π ∫ from 1 to 2 of (6^2 - (y^2+2)^2) dy. The user seeks confirmation on the accuracy of these calculations. The discussion emphasizes the importance of correct application of integration techniques in volume calculations.
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 ...
$\displaystyle V = \pi \int_0^1 6^2 - (y+2)^2 \, dy + \pi \int_1^2 6^2 - (y^2+2)^2 \,dy$
Hello!
I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem.
Given:
##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0##
##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1##
##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0##
I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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