JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f:[-2,3] \rightarrow[0, \infty)

be a continuous function such that

f(1-x)=f(x)

for all

x \in[-2,3]

.
If

R_1

is the numerical value of the area of the region bounded by

y=f(x), x=-2, x=3

and the axis of

x

and

R_2=\int_{-2}^3 x f(x) d x

, then:

View answer and explanation

Correct option: D

\mathrm{R}_1=2 \mathrm{R}_2

Option D (

\mathrm{R}_1=2 \mathrm{R}_2

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

f(1-x)=f(x)

, we can show that

2R_2 = R_1

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