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Definite Integration question

2015 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Definite Integration
2015 · Shift 2 · Q36

Definite Integration question

2015 · Shift 2 · Q36

JEE AdvancedMathematicsDefinite IntegrationMCQ+4 / −1

Let

f'\left( x \right) = {{192{x^3}} \over {2 + {{\sin }^4}\,\pi x}}

for all

x \in R\,\,

with

f\left( {{1 \over 2}} \right) = 0

. If

m \le \int\limits_{1/2}^1 {f\left( x \right)dx \le M,}

then the possible values of

m

and

M

are

A
$m=13,M=24$
B
$\,m = {1 \over 4},M = {1 \over 2}$
C
$m=-11,M=0$
D
$m=1,M=12$

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