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Problem 19

In Exercises $19-22,$ find the work done by $F$ o…

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Problem 18

Along the curve $\mathbf{r}(t)=(\cos t) \mathbf{i}+(\sin t) \mathbf{j}-(\cos t) \mathbf{k}, 0 \leq t \leq \pi$
evaluate each of the following integrals.
\begin{equation}
\text {a. }\int_{C} x z d x \quad \text { b. } \int_{C} x z d y \quad \text { c. } \int_{C} x y z d z
\end{equation}

Answer

(a) $\frac{2}{3}$
(b) 0
(c) $-\frac{\pi}{8}$


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Video Transcript

a problem. 18. Actually, it's called 90 thes minus costs 90 so that this can be changed into one toe, minus one minus X squared DX. Right. So that's one or three minus. I just won over three. So it's plus one or three. So it is to over three for the second part. Oh, that's, uh, co sign T Square minus 90 Squire d sci fi. Okay, that is people's toe sign. He square minus one society. Right. So can change from 0 to 0. Oh, so that's a zero now from 00 x square, minus one. Need X. If you change acts into sci fi. So that's a zero His because science, you're always equals Sign pi, then four parts three. We cannot use the tricks here. So this actually x y z is minus. I he course I Inti Square and disease. Just, uh, the cause. I nt t minus called Sci Fi. So that's science TV. So we have a square here and just GT he runs a rose. Hi. We know that it that is one or two. I'm sai toe t square minus. Yeah, right. And mmm. So we have minus one force on change this into to bind miners house I 40 e p right from heroes with pie. So as for this part, this is off course pipe erotic. So that's a zero when takes integral. So the answer is minus one or eight. Just this first term. Oh, pipes, or I get a pie.

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