Elliptic integrals The length of the ellipse
x=acost,y=bsint,0≤t≤2π
turns out to be
=4a∫π/201−e2cos2t√dt
where e is the ellipse's eccentricity. The integral in this formula, called an elliptic integral, is non elementary except when e=0 or 1 a. Use the Trapezoidal Rule with n=10 to estimate the length of the ellipse when a=1 and e=1/2 . b. Use the fact that the absolute value of the second derivative of f(t)=1−e2cos2t√ 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
How many coulombs of charge pass a cross section of the wire in the time interval between
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.