Line integral anyone?

Calculus Level 1

A line integral is a definite integral where you integrate some function $f(x,y,z)$ along some path. For which of the following would it be appropriate to use a line integral?

A. The total work done on a charge moving in a circle of radius $R$ on the $xy$ -plane centered at the $z$ -axis by a charge at the coordinate $(R,R,R)$

B. The area under the curve $y=x^2$ between $x=2$ and $x=5$

C. The total radiation absorbed by a person walking at a uniform rate around an ellipse with minor axis of length $a$ and major axis of length $b$ , with a radiation source at the coordinate $(b,a)$

A only A and B A and C B only B and C C only All of them None of them

2 solutions

Geoff Pilling
Dec 30, 2016

For A and C you need to integrate a function along a path. However, for B you just need to perform a standard integration, namely $\int_2^5x^2dx$ .

Therefore, a line integral is only really necessary for $\boxed{\text{A and C}}$ .

You don't have to use a line integral for B, but you could. I would suggest to reword the question, because appropriate does not mean necessary.

peter teloff - 3 years, 1 month ago

Hmmm... Good point... Lemme think about how I could state the question better...

Geoff Pilling - 3 years ago

Vote for peter.

Xumeng Chen - 2 years, 2 months ago

Ricardo Re
Apr 15, 2020

A path integral is used when you have a function that describes a path and have things that varys as functions of the move in the path

Line integral anyone?

2 solutions

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