JEE Advanced 2015 Paper 2 Mathematics Q16

Mathematics

Problem

Let

f'(x)=\dfrac{192x^3}{2+\sin^4\pi x}

for all

x\in\mathbb R

with

f\left(\dfrac12\right)=0

. If

m\le\displaystyle\int_{1/2}^{1}f(x)\,dx\le M

, then the possible values of

m

and

M

are