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Question

If f(x)=f(ax), then a0f(x)dx is equal to

A
a0f(x)dx
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B
a22a0f(x)dx
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C
a2a0f(x)dx
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D
a2a0f(x)dx
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Solution

The correct option is C a2a0f(x)dx
Let I=a0xf(x)dx ......(i)
I=a0(ax)f(ax)dx
I=a0(ax)f(x)dx[f(x)=f(ax)given]
I=aa0f(x)dxa0xf(x)dx .....(ii)
On adding equations (i) and (ii), we get
2I=aa0f(x)dx
I=a2a0f(x)dx

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