[See Steps] Let S be the part of the plane z=2 x+y+5 inside the cylinder x^2+y^2=1 with normal oriented upwards, and let \boldsymbolF:=x i-z j-y k Compute
Question: Let \(S\) be the part of the plane \(z=2 x+y+5\) inside the cylinder \(x^{2}+y^{2}=1\) with normal oriented upwards, and let \(\boldsymbol{F}:=x \mathbf{i}-z \mathbf{j}-y \mathbf{k}\)
- Compute the area of \(S\)
- Compute \(\iint_{S}{\mathbf{F}}\cdot d~\text{S}\)
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(Solved) Let C be the straight line segment from (1,0,1) to (2,2,3)
![[Solution] Let F:=(2 x-y) i+(e^z-x) j+y e^z](/images/solutions/MC-solution-library-46786.jpg "[Solution] Let F:=(2 x-y) i+(e^z-x) j+y e^z k and let C be the")
[Solution] Let F:=(2 x-y) i+(e^z-x) j+y e^z k and let C be the
![[Solved] Let C be the closed curve](/images/solutions/MC-solution-library-46787.jpg "[Solved] Let C be the closed curve obtained by intersecting the paraboloid")
[Solved] Let C be the closed curve obtained by intersecting the paraboloid
![[Solved] Crickets make their chirping sounds by](/images/solutions/MC-solution-library-46788.jpg "[Solved] Crickets make their chirping sounds by rapidly sliding one")
[Solved] Crickets make their chirping sounds by rapidly sliding one
Solution: Consider the following data on energy consumption.
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