I am struggling to get the correct answer for the question:
What is the magnitude of the displacement of a particle moving in the $x$-$y$ plane with the velocity vector given by $v(t) = (e^{\sin t}, 5t^2)$ for time $t \ge 0$ between time $t=1$ and $t=2$.
I attempted to take the integral of the speed function $\int_1^{2} (\sqrt{e^{2\sin t}+25t^4}) \, \mathrm{d}t \\$ since the velocity of the particle is always positive on the interval and got the answer $11.992$. However, apparently the correct answer is $11.954$, but I can't find a way to come about that answer.
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