= curl F. ñ ds. I NEED IT SOLVED AGAIN USING THE CURL METHOD Calculate the total effect of the wind (W(x, y, z) = (z, a², y)) along Guido's path P = (2 cos(t), 2 sin(t), t) for t = [0, 8].
= curl F. ñ ds. I NEED IT SOLVED AGAIN USING THE CURL METHOD Calculate the total effect of the wind (W(x, y, z) = (z, a², y)) along Guido's path P = (2 cos(t), 2 sin(t), t) for t = [0, 8].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I have provided the formula needed for the Stokes theorem problem please solve with the curl method the answer is 16pi
I have two show the solution both ways/methods. SO PLEASE SETUP AND SOLVE THE CURL METHOD FOR STOKES it would mean a lot to me.
![= J₁₂² curl F. ñ ds.
I NEED IT SOLVED AGAIN USING THE CURL METHOD
Calculate the total effect of the wind (W(x, y, z) = (z, x², y)) along Guido's path
P = (2 cos(t), 2 sin(t), t) for t = [0, 8].
Step 2: Calculation
Path can be written in parametric form
x=2cost, y= 2sint, z=t
→dx= -2sintdt, dy = 2 cost dt, dz=dt
Now
IN-dy = zdz + x²dy + y dz
WW.dr
W.dr
IN dr
=
=
"1
2
z (-2Bintdt) + x² (2 costdb) +ydt
t (-2sintdt) +
The total effect of the wind
8TT
=
SW.dr = S(-2tsint + 8 cas³t+2 sint) dt
P
= (-2tsint+scost+ 2gint) dt
T
»
+ (2cost)² (2 costdt) + 2 sint d
0
8TT
YTT
8m
[(-2t sint) dt + 85 cosst-scostd+(29intdt
8TT
8TT
8m
815
-2ftsintdt + 2 Scosst - 5 Scostdt +2 f sint dt
0
0
#
= -2 ft cost
16 TT
IT
RIT
-6
int ] Ⓡ " + 2 [ singt " " 6 [sint]["+" (-2cost]"
+
-
3
O
-21 -8 IT cos BπT + singπT-0] + 2[singulT]-csing πT-2 [COS BIT-coso]
-2 [-8 IT +0 -0] + 2 [] - 6x0-2 [1-1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe624ad94-7daf-4780-83ae-289c842fe4c5%2Fa07b0d0f-ee73-402a-98f3-37ae6cd43513%2Fsuhwvx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:= J₁₂² curl F. ñ ds.
I NEED IT SOLVED AGAIN USING THE CURL METHOD
Calculate the total effect of the wind (W(x, y, z) = (z, x², y)) along Guido's path
P = (2 cos(t), 2 sin(t), t) for t = [0, 8].
Step 2: Calculation
Path can be written in parametric form
x=2cost, y= 2sint, z=t
→dx= -2sintdt, dy = 2 cost dt, dz=dt
Now
IN-dy = zdz + x²dy + y dz
WW.dr
W.dr
IN dr
=
=
"1
2
z (-2Bintdt) + x² (2 costdb) +ydt
t (-2sintdt) +
The total effect of the wind
8TT
=
SW.dr = S(-2tsint + 8 cas³t+2 sint) dt
P
= (-2tsint+scost+ 2gint) dt
T
»
+ (2cost)² (2 costdt) + 2 sint d
0
8TT
YTT
8m
[(-2t sint) dt + 85 cosst-scostd+(29intdt
8TT
8TT
8m
815
-2ftsintdt + 2 Scosst - 5 Scostdt +2 f sint dt
0
0
#
= -2 ft cost
16 TT
IT
RIT
-6
int ] Ⓡ " + 2 [ singt " " 6 [sint]["+" (-2cost]"
+
-
3
O
-21 -8 IT cos BπT + singπT-0] + 2[singulT]-csing πT-2 [COS BIT-coso]
-2 [-8 IT +0 -0] + 2 [] - 6x0-2 [1-1]
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