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Question

Consider the function f(x) and g(x) on R, defined as f(x)=2xx2 and g(x)=xn where nN. If the area between y=f(x) and y=g(x) in the first quadrant is 12 sq. unit, then n is a divisor of

A
12
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B
15
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C
20
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D
30
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Solution

The correct option is D 30
Given f(x)=2xx2 and g(x)=xn
To get intersection points, solving f(x) and g(x)
we have 2xx2=xn
x=0 and x=1


Area =10(f(x)g(x))dx
=10(2xx2xn)dx
=[x2x33xn+1n+1]10
=[1131n+1]=231n+1

Now, 231n+1=12
16=1n+1
n+1=6n=5
Hence, n is divisor of 15,20,30

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