Let F ( x ) = sin x ∫ 0 x cos t d t + 2 ∫ 0 x t d t + cos 2 x − x 2 . Then the area bounded by x F ( x ) and the ordinates x = 0 and x = 5 with the x-axis is

Question

Let F ( x ) = sin x ∫ 0 x ​ cos t d t + 2 ∫ 0 x ​ t d t + cos 2 x − x 2 . Then the area bounded by x F ( x ) and the ordinates x = 0 and x = 5 with the x-axis is

TestHub · Accepted Answer

F ( x ) = sin x ( sin x ) + 2 ( 2 x 2 ​ ) + cos 2 x − x 2 = sin 2 x + x 2 + cos 2 x − x 2 = 1 . Hence area = ∫ 0 5 ​ x F ( x ) d x = ∫ 0 5 ​ x d x = [ 2 x 2 ​ ] 0 5 ​ = 2 25 ​ .

Mathematics - Area Under Curves Question with Solution | TestHub

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