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Question

Let f:(0, 1]R be a continuous function such that π0f(sin x) dx=2018, then π0x f(sin x) dx is equal to

A
1009π
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B
1008π
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C
2017π
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D
2016π
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Solution

The correct option is A 1009π
Let I=π0x f(sin x) dxI=π0(πx) f(sin (πx)) dxI=π0(πx) f(sin x) dxI=ππ0f(sin x) dxπ0x f(sin x) dx2 I=ππ0f(sin x) dx=2018πI=1009π

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