Mathathon 2020 Problem 6 − - Hard

Calculus Level 3

f ( x ) = x 2 + 4 3 \large f(x) = \sqrt[3]{x^{2} + 4}

Let g ( x ) g(x) be an antiderivative of f ( x ) f(x) above. If g ( 5 ) = 7 g(5) = 7 , find the value of g ( 1 ) g(1) to two decimal places.


The answer is -2.44.

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1 solution

No one has posted a solution yet!!!!!

@Hamza Anushath , @Siddharth Chakravarty , @Alak Bhattacharya

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The given answer (-2.44) is wrong. The numerical value of the integral of (x^2 + 4x)^(1/3) dx from 1 to 5 is 10.88... (see WolframAlpha), so g(1) = g(5) - 10.88... = 7 - 10.88... = -3.88... On the other hand, if f(x) = (x^2 + 4)^(1/3), then the integral of f(x) dx from 1 to 5 is 9.44... (see WolframAlpha again), so in this case g(1) = -2.44...

Ricardo Moritz Cavalcanti - 10 months, 3 weeks ago

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He had previously posted a problem where there was +4 rather +4x and thus the confusion had arisen.

Siddharth Chakravarty - 10 months, 3 weeks ago

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