Let f ( x ) = max { x + ∣ x ∣ , x − [ x ]} , where [ x ] stands for the greatest integer not greater than x . Then ∫ − 3 3 f ( x ) d x has the value

Question

Let f ( x ) = max { x + ∣ x ∣ , x − [ x ]} , where [ x ] stands for the greatest integer not greater than x . Then ∫ − 3 3 ​ f ( x ) d x has the value

TestHub · Accepted Answer

​ f ( x ) = max ⋅ { x + ∣ x ∣ , x − [ x ]} = max { x + ∣ x ∣ , { x }} ∫ − 3 3 ​ f ( x ) d x = ∫ − 3 0 ​ { x } d x + ∫ 0 3 ​ 2 x d x = 2 3 ​ + 9 = 2 21 ​ ​

Mathematics - Area Under Curves Question with Solution | TestHub

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