Find the value of integral $\int_C (x + y + z)ds$, where $C$ is parmeterized by $\vec{r}(t) = (9\sin(2t), 7\cos(2t), 4\sqrt{2}\cos(2t))$ for $0 \le t \le \pi$.
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In this case, ds is given by: ds = sqrt((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2) dt where dx/dt, dy/dt, and dz/dt are the derivatives of x, y, and z with respect to t, respectively. In this case, we have: dx/dt = 7 dy/dt = 18cos(2t) dz/dt = -14sin(2t) ds = sqrt(7^2 Show more…
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