Question

Question 8: Assume the drive flies in the gravitational field \textbf{F}(x, y, z) = [x^7 + xy^2z^2, x^2yz^2, x^2y^2z] along the path $C: \textbf{r}(t) = [t \cos t, t \sin t, t(5\pi - t)]$ with $0 \le t \le 5\pi$. (a) Compute the work $\int_0^{5\pi} \textbf{F} \cdot d\textbf{r}$. (b) Compute $d = \left| \int_0^{5\pi} \textbf{r}'(t)dt \right|.$

          Question 8: Assume the drive flies in the gravitational field
\textbf{F}(x, y, z) = [x^7 + xy^2z^2, x^2yz^2, x^2y^2z]
along the path $C: \textbf{r}(t) = [t \cos t, t \sin t, t(5\pi - t)]$ with $0 \le t \le 5\pi$.
(a) Compute the work $\int_0^{5\pi} \textbf{F} \cdot d\textbf{r}$.
(b) Compute $d = \left| \int_0^{5\pi} \textbf{r}'(t)dt \right|.$

Question 8: Assume the drive flies in the gravitational field
F(x, y, z) = [x^7 + xy^2z^2, x^2yz^2, x^2y^2z]
along the path C: r(t) = [t cos t, t sin t, t(5π - t)] with 0 ≤ t ≤ 5π.
(a) Compute the work ∫0^5πF· dr.
(b) Compute d = | ∫0^5πr'(t)dt |.

Added by Alicia E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Israel Hernandez

07/10/2022

Step 1

r'(t) = [-tsint, tcost, 5π - t] Show more…

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Question 8: Assume the drive flies in the gravitational field F(x,y,z)=[x^(7)+xy^(2)z^(2),x^(2)yz^(2),x^(2)y^(2)z] along the path C:r(t)=[tcost,tsint,t(5pi -t)] with 0<=t<=5pi . (a) Compute the work ∫_0^(5pi ) F*dr. (b) Compute d=|∫_0^(5pi ) r'(t)dt|.