JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

f(a + b + 1 - x) = f(x)

, for all x, where a and b are fixed positive real numbers, then

\frac{1}{{a + b}}\,\int_a^b {x(f(x) + f(x + 1))dx}

is equal to

View answer and explanation

Correct option: C

\int_{a - 1}^{b - 1} {f(x + 1)dx}

Option D (

\int_{a - 1}^{b - 1} {f(x + 1)dx}

) is correct because by using the given property and applying integration properties, the integral simplifies to the given form.

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