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

1. Mar 27, 2006

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)?

2. Mar 27, 2006

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.

3. Mar 27, 2006

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?

4. Mar 28, 2006

HallsofIvy

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

5. Mar 28, 2006

arildno

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