KVPY SX SB Exam 05-Nov-2017 Question Paper

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Question : 8 of 120

Marks: +1, -0

The parabola

y^2 = 4x + 1

divides the disc

x^2+ y^2≤ 1

into two regions with areas

A_1

and

A_2

. Then

| A_1 -A_2 |

equals

$1/3$
$2/3$
$π/4$
$π/3$

Solution:

A_1 = 2∫↖{0}↙{-1\/4}√{4x+1}dx

+2∫↖{1}↙{0}√{1-x^2}dx

Solve

A_1 = 1/3+π/2

A_2 = π(1)^2-A_1 =π/2-1/3

| A_1 -A_2 |=2/3

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