# Homework Help: Fundamental theory of calculus

1. Apr 7, 2012

### Froskoy

1. The problem statement, all variables and given/known data
The question:

The function F(θ,k) is defined as

$$F(\theta,k)=\int_0^θ (f(x,k))\mathrm{d}x$$

Find expressions for $\left({\frac{\partial F}{\partial \theta}}\right)_k$ and $\left({\frac{\partial F}{\partial k}}\right)_θ$

2. Relevant equations
Fundamental theory of calculus
Chain rule?

3. The attempt at a solution
I think $\left({\frac{\partial F}{\partial \theta}}\right)_k$ is just $f(\theta,k)$ - is that correct? or is it $f(\theta,0)$ because $k$ is held constant so when it is differentiated it will be 0.

I'm a little stumped by the second part. Is there some way to re-express it in terms of $\left({\frac{\partial F}{\partial\theta}}\right)_k$ using the chain rule?

2. Apr 7, 2012