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Question

Let f and g be continuous function on [0,a] such that f(x)=f(ax) and g(x)+g(ax)=4, then a0f(x)g(x)dx is equal to :

A
a0f(x)dx
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B
2a0f(x)dx
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C
4a0f(x)dx
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D
3a0f(x)dx
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Solution

The correct option is B 2a0f(x)dx
Given f(x)=f(ax)
g(x)+g(ax)=4g(ax)=4g(x)
I=a0f(x).g(x)dx
=a0f(ax).g(ax)dx
=a0f(x).(4g(x))dx
I=a04f(x)dxa0f(x).g(x)dx
2I=a04f(x)dx
I=2a0f(x)dx

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