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YZ

# Integrate $f ( x , y , z ) = - \sqrt { x ^ { 2 } + z ^ { 2 } }$ over the circle$$\mathbf { r } ( t ) = ( a \cos t ) \mathbf { j } + ( a \sin t ) \mathbf { k } , \quad 0 \leq t \leq 2 \pi$$

## $-4 a^{2}$

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### Video Transcript

So now we have the path far T Biggles. Two ankles. Aunty, I'm sorry. First entry zero zero, then a consistency. Then they signed C and two's from Ah, there's a two ply. Okay, So the derivative of the batter will be not a sign t in equals aunty. And what's gonna be the marshal if it Let's see. So it's simply a or actually it's after the value of because there's no information known the positivity of a Okay, So our path is a girl. Yes, well, in close to zero through ploy 02 ply so that if a mortal squared Santy did she close the other port, which is pi to two pi. And here we have sensitivity. So it's Theo the opposite. And now we have the answer for the Sioux Integral Wishes. Next way squared minus a squared and then minus. They scored. Closest. Weird. So this is like a voice where

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University of Illinois at Urbana-Champaign

Integrals

Vectors

Vector Functions

Lectures

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