How do you find the arc length of the curve given by the parametric equations below?

Question

How do you find the arc length of the curve given by the parametric equations below, from the point where t = 1 to the point where t = 2.

x = sin t
y = e^t .

these were the possible solutions in the back of the book to choose from....

a. 4.7

b. 23.7

c. 24.1

d. 49.8

or is it none of these ?

Answer 1

The arc length formula is
S = INT[1 to 2] {sqrt( (dy/dt)^2 + (dx/dt)^2 ) dt}

I know that's impossible to read in text; you can see it for real at http://en.wikipedia.org/wiki/Arc_length , you just have to scroll down to the parametric version.

Answer 2

a = dx/dt
b= dy/dt

arc length =
integral of { square root (a^2 +b^2) } dt from t=1 to t=2

Answer 3

dx = cos t dt
dy = e^t dt
ds= sqrt(cos^2t+e^2t) dt
s= Int(1,2) sqrt(cos^2t+e^2t)dt
I don´t see an easy way to calculate this integral