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YZ
Numerade Educator

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Problem 14 Medium Difficulty

Find the line integral of $f ( x , y , z ) = \sqrt { 3 } / \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right)$ over the curve $\mathbf { r } ( t ) = t \mathbf { i } + t \mathbf { j } + t \mathbf { k } , 1 \leq t \leq \infty$

Answer

1

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Video Transcript

Okay, so we have the trajectory or equals two C c n t. And he's from zero eyes from one sweet Billy. So the first thing is gonna we get a derivative off or which it was 2111 So the norman of it People's just square with three and l can transform over London's growing too. And there's a girl with respect t which is the time for andr. So the int'l grants affects Y Z We probably next Wednesday here actually was what it was. He was t We're gonna have one new a square root three times t squared. So here's this. London's a girl will be transformed to one to infinity. When they were scored three t squared attempts The module the norm of d r over DT, which is screwed three and dt service where we have once we've only one over the square TT So this is a indifference in the world. So foreign indebtedness, anger or gonna approach it by the limit if it's of the results of its Chris Morning definite integral result. So here, let's say, um, we have one to be well, beagle so affinity. So the answer is one minus be over one over b and wouldn't be goes to infinity. The answer is simply one

YZ
University of Illinois at Urbana-Champaign
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