Weird Dot Product Homework Q: Unusual Answer?

[wrong_class]

Homework Statement

i have the vector m(x(t), y(t)) = r = (s^t cos(t), e^t sin(t)) and want to find the line integral of it

Homework Equations

1. $$\int m \centerdot r' dt$$
2. $$\int |m| |r'| dt$$

The Attempt at a Solution

the answer is sqrt(2)/2 (e^pi - 1). when i do the problem the first way, i do not get the sqrt(2)
When i do the problem the first way, the answer is wrong, but when i do it the second way, it is correct.

is the first way even correct? i am told it is, but wolfram alpha is agreeing with me

 

[zhermes]

what are m and r, what are the answers you are getting?

 

[Quinzio]

The two integrals are different, why should you get the same result ?

I did the first, assuming m is the vector
$$m = e^t cos\textsl{t}\ \vec{i}+e^t sin\textsl{t}\ \vec{j}$$

$$\int_{0}^{\pi \over 2} m\cdot m' dt = {e^\pi \over 2}- {1 \over 2 }$$

One the second one it is likely a sqrt to pop up.

 

[wrong_class]

so the integrals are different. So why did someone who learned this already tell me these two are the same?

thats the answer I am getting.

thanks!

 

[wrong_class]

can someone clarify this for me?:

given r(t) is a vector, how do you find the line integral if f(x(t),(y(t)) returns a scalar? A vector? do you always get 2 scalars (magnitude of f and magnitude of r' ) and multiply them? do you take the gradient if f is scalar and then dot deL_f and r' ?