KVPY SX SB Exam 2013 Question Paper

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Question : 14 of 120

Marks: +1, -0

The area bounded by the curve

y = \cos x

, the line joining

(-π/4, \cos(-π/4))

and (0, 2) and the line joining

(π / 4, cos(π/4))

and (0, 2) is

$({4+√2}/8)π-√2$
$({4+√2}/8)π+√2$
$({4+√2}/4)π-√2$
$({4+√2}/4)π+√2$

Solution:

required area

=2[1/2(1/√2+2)\π/4-∫↖{\π\/4}↙{0}\cos x\dx]

=({4+√2}/8)\π-√2

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