The conic for the equation displaystyle{left({x}+{2}right)}^{2}+{left({y}-{1}right)}^{2}={4} and also describe the translation of the conic from the standard position.

Elliptic integrals The length of the ellipse

x=acost,y=bsint,0≤t≤2π$$x=a\cos t,y=b\sin t,0\le t\le 2\pi$$

turns out to be

=4a∫π/201−e2cos2t√dt$$=4a{\int }_0^{\pi /2}\sqrt{1-e^2{\cos }^{2}t}dt$$

where e$e$ is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is non elementary except when e=0$e=0$ or 1 a. Use the Trapezoidal Rule with n=10$n=10$ to estimate the length of the ellipse when a=1$a=1$ and e=1/2$e=1/2$ . b. Use the fact that the absolute value of the second derivative of f(t)=1−e2cos2t√$f(t)=\sqrt{1-e^2{\cos }^{2}t}$ is less than 1 to find an upper bound for the error in the estimate you obtained in part (a).

The current in a wire varies with time according to the relation $I=55A?(0.65A/s^2)t^2$.
How many coulombs of charge pass a cross section of the wire in the time interval between $t=0$ and $t=8.5s$ ?
Express your answer using two significant figures.
What constant current would transport the same charge in the same time interval?
Express your answer using two significant figures.