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Multivariable Calculus

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Moderate

Scalar Line Integral on Helix

MVCALC-AVXY21

Evaluate the scalar line integral:

$$I = \int_{C} (x^2 + \frac{y}{2}) ds$$

...when $C$ is the helix (see Figure):

$$ \vec{r}(t) = (\cos t, \sin t, t), t \in [0, 2\pi]$$

A

$\cfrac{\sqrt{2}\pi}{2}$

B

$2\sqrt{2}\pi$

C

$2\pi$

D

$\sqrt{2}\pi$

E

$\sqrt{\pi}$