Areas Under Curves
The area bounded by y = x² and y = x from x = 0 to x = 1 is
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About This Question
- Subject
- mathematics
- Chapter
- integral calculus
- Topic
- areas under curves
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
1/6 square units
- Identify Upper and Lower Curves: On the interval (0,1), x≥x2. So y=x is the upper curve and y=x2 is the lower curve.
- Setup Area Integral: Area=∫01(Upper−Lower)dx=∫01(x−x2)dx.
- Antiderivative: [2x2−3x3]01
- Evaluate:
- (21−31)−(0−0)
- =63−2=1/6.
- Result: 1/6 square units.
This medium difficulty mathematics question is from the chapter integral calculus, covering the topic of areas under curves. It appeared in the 2025 exam.
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