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Q.

Let f(x) be a continuous function such that the area bounded  by the curve y=f(x),x -axis and the lines x=0 and x=a is a22+a2sina+π2cosa, then fπ2

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Detailed Solution

We have, ∫0af(x)dx=a22+a2sina+π2cosaDifferentiate both sides f(a)=a+12(sina+acosa)−π2sina Put a =π2;fπ2=π2+12−π2=12
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