Question

Which of the following functions is/are Riemann integrable on [0, 1] ?

• A. $f(x)=\int\limits^x_0|\frac{1}{2}-t|dt$
• B. $f(x)=\begin{cases}  x \sin(1/x) & \text{if }x \ne0 \\     0 & \text{if }x=0 \end{cases}$
• C. $f(x)=\begin{cases} 1 & \text{if }x \in Q ∩[0,1] \\     -1 & \text{otherwise} \end{cases}$
• D. $f(x)=\begin{cases} x & \text{if }x \in [0,1) \\     0 & \text{if } x=1\end{cases}$

Answer 1

The Correct Option is A, B, D

The correct option is (A) : $f(x)=\int\limits^x_0|\frac{1}{2}-t|dt$, (B) : $f(x)=\begin{cases}  x \sin(1/x) & \text{if }x \ne0 \\     0 & \text{if }x=0 \end{cases}$ and (D) : $f(x)=\begin{cases}   x & \text{if }x \in [0,1) \\     0 & \text{if } x=1\end{cases}$