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Definite Integration question

2023 · 29 Jan · Shift 1 · Q28

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PYQ Library
JEE Main
Mathematics
Definite Integration
2023 · 29 Jan · Shift 1 · Q28

Definite Integration question

2023 · 29 Jan · Shift 1 · Q28

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f(x) = x + {a \over {{\pi ^2} - 4}}\sin x + {b \over {{\pi ^2} - 4}}\cos x,x \in R

be a function which satisfies

f(x) = x + \int\limits_0^{\pi /2} {\sin (x + y)f(y)dy}

. then

(a+b)

is equal to

A
$- 2\pi (\pi + 2)$
B
$- \pi (\pi - 2)$
C
$- \pi (\pi + 2)$
D
$- 2\pi (\pi - 2)$

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