For 2 ≤ x ≤ 4 , let f ( x ) = max { 4 − x 2 , ∣ x − 2∣ , ( x − 2 ) 1/3 } . The area between this curve and the x -axis is p / q , where p , q are coprime. Find p + q .

Question

For 2 ≤ x ≤ 4 , let f ( x ) = max { 4 − x 2 , ∣ x − 2∣ , ( x − 2 ) 1/3 } . The area between this curve and the x -axis is p / q , where p , q are coprime. Find p + q . ​

TestHub · Accepted Answer

f ( x ) = max { 4 − x 2 , ∣ x − 2∣ , ( x − 2 ) 1/3 } ​ for x ∈ [ 2 , 4 ] S = ∫ 2 3 ​ ( x − 2 ) 1/3 d x + ∫ 3 4 ​ ( x − 2 ) d x = 4 3 ​ + 2 3 ​ = 4 9 ​ . ​ So p + q = 13

Mathematics - Area Under Curves Question with Solution | TestHub

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