Area Between Curves Worksheet
A Grade 10 Math worksheet covering the calculation of area between curves using integration.
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Area Between Curves
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Read each question carefully and show all your work. Calculate the area between the given curves.
1. Find the area of the region bounded by the curves y = x² and y = x.
2. Calculate the area of the region enclosed by the parabolas y = x² and y = 2x - x².
3. To find the area between two curves, f(x) and g(x), where f(x) ≥ g(x) over an interval [a, b], we use the definite integral from a to b of dx.
4. The area between curves can sometimes be negative, indicating the lower function is above the upper function.
True
False
5. Which of the following represents the area between y = sin(x) and y = cos(x) from x=0 to x=π/2?
∫ (cos(x) - sin(x)) dx from 0 to π/2
∫ (sin(x) - cos(x)) dx from 0 to π/2
| ∫ (cos(x) - sin(x)) dx from 0 to π/2 |
∫ |cos(x) - sin(x)| dx from 0 to π/2
6. Determine the area of the region bounded by x = y² and x = y + 2.