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Question

Let f(x)=192x3(2+sin4(nπ)) for all xR with f(1/2)=0. If m11/2f(x)dxM , then the possible values of m and M are

A
m=13,M=24
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B
m=1/4,M=1/2
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C
m=11,M=0
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D
m=1,M=12
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Solution

The correct options are
A m=13,M=24
D m=1,M=12
192x33<f(x)<192x32
16(x4116)<x12f(x)dx<24(x4116)
16(x55x16)112<x12f(x)dx<24(x55x16)112
2.6<x12f(x)dx<3.9
Hence, only possible option is D.

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