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Definite Integration question

2020 · 7 Jan · Shift 1 · Q38

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PYQ Library
JEE Main
Mathematics
Definite Integration
2020 · 7 Jan · Shift 1 · Q38

Definite Integration question

2020 · 7 Jan · Shift 1 · Q38

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then

{1 \over {a + b}}\int_a^b {x\left( {f(x) + f(x + 1)} \right)} dx

is equal to:

A
$\int_{a - 1}^{b - 1} {f(x+1)dx}$
B
$\int_{a + 1}^{b + 1} {f(x + 1)dx}$
C
$\int_{a - 1}^{b - 1} {f(x)dx}$
D
$\int_{a + 1}^{b + 1} {f(x)dx}$

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