# Vector Calc: Can you verify my answer?

1. Jun 7, 2009

### rsq_a

Just looking for a yes/no. I worked out the following question:

I got,

(A) $$e^2$$
(B) $$\pi$$
(C) $$-(1+3\pi/2, 1+3\pi/2, 0)$$

Did I hit the mark?

Last edited: Jun 8, 2009
2. Jun 7, 2009

### HallsofIvy

Staff Emeritus
I haven't done (C) yet but I don't get anything like you have for either (A) or (B). Show how you got those answers.

3. Jun 7, 2009

### rsq_a

Okay. So for (A):

\begin{align*}L &= \int_1^e |r'(t)| dt \\ &= \int_1^e |(1/t, 2, 2t)| dt \\ &= \int_1^e \sqrt{\frac{(2t^2+1)^2}{t^2}} dt = \int_1^e 2t + \frac{1}{t} dt \\ &= e^2 - 1 + 1 = e^2\end{align*}

For (B), the contour is,

$$\gamma(t) = (\cos t, \sin t, 2\cos t + 1)$$

So the relevant integral is,

$$\int_0^{2\pi} (\sin t, 2 \sin t + 1, \cos t) \cdot (-\sin t, \cos t, -2 \cos t) \ dt = \pi$$

Does that look wrong?

Last edited: Jun 8, 2009
4. Jun 8, 2009

### daudaudaudau

In (B), if you say that y=sin(t), then you should find z=2*y+1=2*sin(t)+1, right?

5. Jun 8, 2009

### rsq_a

Doh! But I think the answer is the same. I've corrected it in the post above.