Question

Evaluate the following line integral along the curve C . \[ \int_{C}(y-z) d s ; C \text { is the helix }\langle 5 \cos t, 5 \sin t, t\rangle \text {, for }-2 \pi \leq t \leq 0 \] The value of the integral is \( \square \) . (Type an exact answer, using radicals as needed.)

          Evaluate the following line integral along the curve C .
\[
\int_{C}(y-z) d s ; C \text { is the helix }\langle 5 \cos t, 5 \sin t, t\rangle \text {, for }-2 \pi \leq t \leq 0
\]

The value of the integral is \( \square \) .
(Type an exact answer, using radicals as needed.)

Evaluate the following line integral along the curve C .

∫C(y-z) d s ; C is the helix ⟨ 5 cos t, 5 sin t, t⟩, for -2 π≤ t ≤ 0

The value of the integral is □ .
(Type an exact answer, using radicals as needed.)

Added by Katrina F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Minh Le

Step 1

The curve \( C \) is given by the helix: \[ \mathbf{r}(t) = \langle 5 \cos t, 5 \sin t, t \rangle \] for \( -2\pi \leq t \leq 0 \). Show more…

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Evaluate the following line integral along the curve C . \[ \int_{C}(y-z) d s ; C \text { is the helix }\langle 5 \cos t, 5 \sin t, t\rangle \text {, for }-2 \pi \leq t \leq 0 \] The value of the integral is \( \square \) . (Type an exact answer, using radicals as needed.)