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Multivariable Calculus

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Scalar Line Integral with 2D Parametric Curve

MVCALC-DTLLJ4

Let $\phi(x,y)=xe^y-2y$, $\vec{F}=\nabla \phi$. Evaluate the line integral:

$$I=\int_C \vec{F}\cdot \vec{T}\, ds$$

...along the curve $C$ given in parametric form:

$$\vec{r}(t)= \langle te^t, t+2\rangle, t\in[0,1]$$

A

$-2e^2+1$

B

$2e^2-2$

C

$e^3-2$

D

$e^4-2$

E

$e^3+2$