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 = 4 π and x = β 4 π is ( β sin β + 4 π cos β + 2 β ) . The

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 = 4 π ​ and x = β > 4 π ​ is ( β sin β + 4 π ​ cos β + 2 ​ β ) . Then f ( 2 π ​ ) is

TestHub · Accepted Answer

Given that ∫ π /4 β ​ f ( x ) d x = β sin β + 4 π ​ cos β + 2 β Differentiating w. r. t β f ( β ) = β cos β + sin β − 4 π ​ sin β + 2 ​ f ( 2 π ​ ) = ( 1 − 4 π ​ ) sin 2 π ​ + 2 ​ = 1 − 2 π ​ + 2 ​ .

Mathematics - Area Under Curves Question with Solution | TestHub

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