Consider the parabola and the point

MATHEMATICS · Numerical · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the parabola

y=\frac{x^2}{4}

and the point

F(0,1)

. Let

A_1(x_1,y_1),A_2(x_2,y_2),\ldots,A_n(x_n,y_n)

be points on the parabola such that

x_k>0

and

\angle OFA_k=\frac{k\pi}{2n}

for

k=1,2,\ldots,n

. If

\displaystyle\lim_{n\to\infty}\frac1n\sum_{k=1}^{n}FA_k=\frac{m}{\pi}

, find

m