JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Given that

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

for all

x \in R

. The value

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

is equal to

View answer and explanation

Correct option: D

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

The correct answer is C (

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

) because using the given property and substitution, the integral can be simplified to this form.

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