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Application of Integration question

2011 · Shift 2 · Q28

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PYQ Library
JEE Advanced
Mathematics
Application of Integration
2011 · Shift 2 · Q28

Application of Integration question

2011 · Shift 2 · Q28

JEE AdvancedMathematicsApplication of IntegrationMCQ+4 / −1

Let f

:

\left[ { - 1,2} \right] \to \left[ {0,\infty } \right]

be a continuous function such that

f\left( x \right) = f\left( {1 - x} \right)

for all

x \in \left[ { - 1,2} \right]

Let

{R_1} = \int\limits_{ - 1}^2 {xf\left( x \right)dx,}

and

{R_2}

be the area of the region bounded by

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

and the

x

-axis. Then

A
${R_1} = 2{R_2}$
B
${R_1} = 3{R_2}$
C
${2R_1} = {R_2}$
D
${3R_1} = {R_2}$

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