JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Hard

1 of 1

Analyzing +4 | -1

Let

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

be a continuous function such that

f(x)=f(1-x)

for all

x \in[-1,2]

Let

R_1=\int\limits_{{-1}}^2 x f(x) \,d x

; and

R_2

be the area of the region bounded by

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

and the

x

-axis. Then,

View answer and explanation

Correct option: C

2 R_1=R_2

Option C (

2 R_1=R_2

) is correct because by using the property of definite integrals and the given condition

f(x) = f(1-x)

, we can relate

R_1

and

R_2

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