Prove that $\int_0^1f(x)\,dx=0$ where \begin{equation} f(x)=\left\{\begin{array}{c}1,\,\mbox{if }x=\frac{1}{2}\\ 0,\,\mbox{if }x\neq\frac{1}{2}\end{array}\right. \end{equation} using Riemann sums.
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Lesson Parent:
Problem:
Prove that $\int_0^1f(x)\,dx=0$ where
\begin{equation}
f(x)=\left\{\begin{array}{c}1,\,\mbox{if }x=\frac{1}{2}\\ 0,\,\mbox{if }x\neq\frac{1}{2}\end{array}\right.
\end{equation}
using Riemann sums.
Answer:
It is true that $\int_0^1f(x)\,dx=0$ where \begin{equation} f(x)=\left\{\begin{array}{c}1,\,\mbox{if }x=\frac{1}{2}\\ 0,\,\mbox{if }x\neq\frac{1}{2}\end{array}\right.\end{equation}
