## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

(11.33)

converges uniformly for $y\in \left[c\text{,}d\right]$, then $\phi \in C\left(c\text{,}d\right)$.

Proof

Consider, for example, the case $I=\left[a\text{,}\infty \right)$. Then

$\phi \left(y\right)=\underset{b\to \infty }{\mathrm{lim}}{\int }_{a}^{b}f\left(x\text{,}y\right)\mathit{dx}\text{,}$

where the limit is uniform for $y\in \left[c\text{,}d\right]$. By Theorem 9.34, for every $b>a\text{,}{\int }_{a}^{b}f\left(x\text{,}y\right)\mathit{dx}$ is a continuous function of ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required