Hints on Line Itegrals



Hints on Line Itegrals

[pic]

Case 1. Parametrize and Integrate

a) C is a line joining A and B: Use [pic]

b) C is a circle: Use [pic]

c) C is an Ellipse: Use [pic]

d) C is a Hyperbola: Use [pic]

e) C is a Parabola: Use [pic]

f) C is a Helix: Use [pic]

g) C is given by y=f(x). Use [pic]

Case 2. Stoke’s Theorem

a) In R2, Stoke’s Theorem is called Green’s Theorem. You might as well do every problem referring to Green’s Theorem by using the general Stoke’s theorem formula.

b) In the xy plane , if F=, then ( X F=

c) In the xy plane , dS = , so [pic]

d) In the xz plane, [pic]

e) In the yz plane, [pic]

Case 3. Easy. Find the potential f and evaluate at the end points.

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W=0

[pic] [pic]

[pic]

Parametrize and Integrate

Yes

No

Yes

No

Is C closed?

Is C closed?

Yes

No

Is [pic]

[pic]

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