Area Under Curves
Area bounded by the curves y=lnx,y=0, and x=e is:
Log curve area
Select the correct option:
Solution
1
-
Setup Integral: y=lnx intersects y=0 at x=1. The region is from x=1 to x=e. Area =∫1elnxdx.
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Evaluate: Using integration by parts (∫udv), let u=lnx,dv=dx. ∫lnxdx=xlnx−x.
Apply limits: [xlnx−x]1e =(elne−e)−(1ln1−1) =(e−e)−(0−1) =0−(−1)=1.
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About This Question
- Subject
- mathematics
- Chapter
- area under curves
- Topic
- area under curves
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1
-
Setup Integral: y=lnx intersects y=0 at x=1. The region is from x=1 to x=e. Area =∫1elnxdx.
-
Evaluate: Using integration by parts (∫udv), let u=lnx,dv=dx. ∫lnxdx=xlnx−x.
Apply limits: [xlnx−x]1e =(elne−e)−(1ln1−1) =(e−e)−(0−1) =0−(−1)=1.
This easy difficulty mathematics question is from the chapter area under curves, covering the topic of area under curves. It appeared in the 2025 exam.
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