JEE PYQ: Functions Question 40
Question 40 - 2019 (12 Jan Shift 2)
Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x) = f(a-x)$ and $g(x) + g(a-x) = 4$, then $\int_0^a f(x) g(x) , dx$ is equal to:
(1) $4\int_0^a f(x) , dx$
(2) $\int_0^a f(x) , dx$
(3) $2\int_0^a f(x) , dx$
(4) $-3\int_0^a f(x) , dx$
Type: MCQ
Show Answer
Answer: (3) $2\int_0^a f(x) , dx$
Solution
$I = \int_0^a f(x)g(x),dx = \int_0^a f(x)[4-g(x)],dx$
$2I = 4\int_0^a f(x),dx$
$I = 2\int_0^a f(x),dx$
BETA
