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Definite Integration question

2003 · Shift 0 · Q84

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PYQ Library
JEE Main
Mathematics
Definite Integration
2003 · Shift 0 · Q84

Definite Integration question

2003 · Shift 0 · Q84

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

f\left( {a + b - x} \right) = f\left( x \right)

then

\int\limits_a^b {xf\left( x \right)dx}

is equal to

A
${{a + b} \over 2}\int\limits_a^b {f\left( {a + b + x} \right)dx}$
B
${{a + b} \over 2}\int\limits_a^b {f\left( {b - x} \right)dx}$
C
${{a + b} \over 2}\int\limits_a^b {f\left( x \right)dx}$
D
$\,{{b - a} \over 2}\int\limits_a^b {f\left( x \right)dx}$

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