Question:
The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to
The value of $\int_1^4 \log[x]\text{d}x$, where $[x]$ is the greatest integer function is equal to
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Break interval where GIF changes.
Updated On: Apr 26, 2026
- $\log 5$
- $\log 6$
- $\log 2$
- $\log 3$
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The Correct Option is D
Solution and Explanation
Concept:
Break integral into intervals. Step 1: Evaluate. \[ = \int_1^2 \log1 dx + \int_2^3 \log2 dx + \int_3^4 \log3 dx \] \[ = 0 + \log2 + \log3 = \log6 \]
Step 2: Conclusion. Answer = $\log 3$
Break integral into intervals. Step 1: Evaluate. \[ = \int_1^2 \log1 dx + \int_2^3 \log2 dx + \int_3^4 \log3 dx \] \[ = 0 + \log2 + \log3 = \log6 \]
Step 2: Conclusion. Answer = $\log 3$
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