I need to show that, given f:[a,b]-->R where f is Riemann integrable, and F:[a,b]-->R defined by F(x)=$\displaystyle \int^x_a f(t)dt$ prove that F is Lipschitz... kind of stuck on how to approach this.
Any help would be much appreciated, thanks
I need to show that, given f:[a,b]-->R where f is Riemann integrable, and F:[a,b]-->R defined by F(x)=$\displaystyle \int^x_a f(t)dt$ prove that F is Lipschitz... kind of stuck on how to approach this.
Any help would be much appreciated, thanks
Hello.
Recall that $\displaystyle F$ is Lipschitz continuous if there exists a fixed $\displaystyle K>0$ such that for every $\displaystyle x,y\in \mathbb{R}$, $\displaystyle |F(x)-F(y)|\leq K |x-y|$.
Can you think of a way to find such a $\displaystyle K$?