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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Consider a parabola y = (x^2)/(4) and the point F (0, 1) . Let...

Consider a 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), A_3(x_3, y_3), \dots , A_n(x_n, y_n)

are '

n

' points on the parabola such

x_k > 0

and

\angle OFA_k = \frac{k\pi}{2n} (k = 1, 2, 3, \dots , n)

. Then the value of

\lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^n FA_k

, is equal to :

Options

A $\frac{2}{\pi}$
B $\frac{4}{\pi}$
C $\frac{8}{\pi}$
DNone of these

Correct answer

B. $\frac{4}{\pi}$

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