Question:
Which of the following functions is/are Riemann integrable on [0, 1] ?
Which of the following functions is/are Riemann integrable on [0, 1] ?
Updated On: Oct 1, 2024
- \(f(x)=\int\limits^x_0|\frac{1}{2}-t|dt\)
- \(f(x)=\begin{cases} x \sin(1/x) & \text{if }x \ne0 \\ 0 & \text{if }x=0 \end{cases}\)
- \(f(x)=\begin{cases} 1 & \text{if }x \in Q ∩[0,1] \\ -1 & \text{otherwise} \end{cases}\)
- \(f(x)=\begin{cases} x & \text{if }x \in [0,1) \\ 0 & \text{if } x=1\end{cases}\)
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The Correct Option is A, B, D
Solution and Explanation
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) : \(f(x)=\begin{cases} x & \text{if }x \in [0,1) \\ 0 & \text{if } x=1\end{cases}\)
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