Question

3. Evaluate the \"vector valued\" line integral $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y, z) = (x, y, xy)$ and $C$ is given by the parametrization $\mathbf{r}(t) = (\sin t, \cos t, t)$, with $0 \le t \le \pi$. You must evaluate the integral. a) 0 b) $\frac{\pi^2}{2}$ c) $\int_0^{\pi} \sin t \cos t \, dt$ d) $\frac{1}{2} \int_0^{\pi} \sin (2t) \, dt$ e) None of the above.

          3. Evaluate the \"vector valued\" line integral
$\int_C \mathbf{F} \cdot d\mathbf{r}$
where $\mathbf{F}(x, y, z) = (x, y, xy)$ and $C$ is given by the parametrization
$\mathbf{r}(t) = (\sin t, \cos t, t)$, with $0 \le t \le \pi$.
You must evaluate the integral.
a) 0
b) $\frac{\pi^2}{2}$
c) $\int_0^{\pi} \sin t \cos t \, dt$
d) $\frac{1}{2} \int_0^{\pi} \sin (2t) \, dt$
e) None of the above.

3. Evaluate the v̈ector valuedl̈ine integral
𝐅· d𝐫
where 𝐅(x, y, z) = (x, y, xy) and C is given by the parametrization
𝐫(t) = (sin t, cos t, t), with 0 ≤ t ≤π.
You must evaluate the integral.
a) 0
b) (π^2)/(2)
c) ∫0^πsin t cos t dt
d) (1)/(2)∫0^πsin (2t) dt
e) None of the above.

Added by Travis A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

08/07/2022

Step 1

dr is given by the formula: ∫F.dr = ∫F(rt) . rt' dt where F(rt) is the vector field and rt(t) is the parametrization of the curve C. Show more…

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3. Evaluate the vector valued line integral F.dr where Fxy,z=xy,xyand C is given by the parametrization rt=sint,cost,twith0t. You must evaluate the integral. Fxy=<xyx Y(eZSinECoSETE b FarSoF( d fsin2tdt e) None of the above