If f′ is continuous on [0,∞) and \lim_{x\to∞} f(x)=0, then what is \int_{0}^{∞} f′(x)dx?

Question

If f′ is continuous on [0,∞) and \( \lim\limits_{x\to\infty} \) f(x)=0, then what is \( \int\limits_{0}^{\infty} \) f′(x)dx?

Answer 1

Hallo

da f(x1)=\( \int\limits_{0}^{x1}f'(x)dx \)

ist dann \( \int\limits_{0}^{\infty}f'(x)dx \)=0

Gruß lul

Comments

Warum ist denn f(x1)=\( \int\limits_{0}^{x1}f'(x)dx \) ?