Antiderivative of (x^2 + 4x)^(1/3)

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Homework Help Overview

The discussion revolves around finding the antiderivative of the function f(x) = (x^2 + 4x)^(1/3). The original poster expresses difficulty in determining g(1) given that g(5) = 7, indicating a need for clarity on the antiderivative process.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to find the antiderivative G and the importance of including a constant C. There are questions about representing g(1) in terms of g(5) and a definite integral of f, as well as considerations of whether a numerical answer or a formula is preferred.

Discussion Status

Some participants have offered guidance on how to approach the problem, suggesting the use of constants and definite integrals. Multiple interpretations of the problem are being explored, particularly regarding the evaluation of the definite integral.

Contextual Notes

There is an indication that the original poster finds the antiderivative process complex and is unsure about the necessary steps to solve for g(1). The discussion also hints at the possibility of numerical integration as a method for evaluation.

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If f is the function defined by f(x) = (x^2 + 4x)^(1/3) and g is an antiderivative of f such that g(5) = 7 then g(1) =

I thought that I need to find the antiderivative of f but it turns out that it's really messy so I'm not sure, is there something I'm missing to be able to solve for g(1)?
 
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You were on the right track. Find the anti derivative G, and add a constant, C. (Do you know why?) Now choose C such that G(5) = 7. Then find G(1) using the antiderivative plus the C you just found.
 
You already KNOW that g is an anti-derivative of f!
Now, how can you therefore represent g(1) in terms of g(5) and a definite integral of f?
 
Do you want a numerical answer or would g(1)= a formula be sufficient? I think that is what arildno is saying.
 
Agreed:
I can't see any obvious way to evaluate the definite integral other than through numerical integration.
 

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