I am having trouble finding the roots of an integral.
For example $F(c)=\int_a^b{(x^2-c^2)}dx$ for some finite interval $[a,b]$.
The problem is that I am trying to do this using numerical analysis. Obviously the functions is easily integrated.
I guess what I am really trying to ask is what happens if we can not find an antiderivative of the integral how do we find the roots of the integral.
Also is there a routine in matlab one could run to accomplish such a task.
POSSIBLE HINT: If $f$ is integrable in the domain $(a,b)$, the primitive function $F(x)=\int_a^xf(t),dt$ is continuous.
If you want to find $x_0$ such that $F(x_0)=0$ and you cannot compute $F$ explicitely, an idea is to use the theorem that says that if $F(\alpha)$ and $F(\beta)$ have different signs, then there exists $\alpha<\gamma<\beta$ such that $F(\gamma)=0$.