Let f: [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1-x), forall x ∈ [-1, 2]. If R_1 = int_-1^2 x f(x) dx and R_2 are the area of the region bounded by y = f(x), x = -1, x = 2 and the x-axis. Then,

Let f: [-1, 2] → [0, ∞) be a continuous function such that… — JEE Main 2011 Mathematics PYQ

AIEEE 2011

Let

f: [-1, 2] \to [0, \infty)

be a continuous function such that

f(x) = f(1-x), \forall x \in [-1, 2]

. If

R_1 = \int_{-1}^{2} x f(x)\, dx

and

R_2

are the area of the region bounded by

y = f(x), x = -1, x = 2

and the

x

-axis. Then,

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Correct option: C

[AIEEE 2011]

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