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Question

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), x-axis and the ordinates x=π4 and x=β>π4 is βsinβ+π4cosβ+2β. Then f(π2) is

A
(π221)
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B
(π4+21)
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C
π2
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D
(1π42)
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