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

[jesuslovesu]

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)?

 

[seang]

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.

 

[arildno]

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?

 

[HallsofIvy]

Do you want a numerical answer or would g(1)= a formula be sufficient? I think that is what arildno is saying.

 

[arildno]

Agreed:
I can't see any obvious way to evaluate the definite integral other than through numerical integration.