Area Between Curves
This worksheet focuses on calculating the area between two curves using integration, suitable for Grade 11 Calculus students.
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Area Between Curves Worksheet
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Read each question carefully and show all your work. Use integration to find the area of the region bounded by the given curves.
1. Find the area of the region bounded by the curves y = x² and y = 2x - x².
2. Calculate the area of the region enclosed by y = eˣ, y = x, x = 0, and x = 1.
3. To find the area between y = f(x) and y = g(x) from x = a to x = b, where f(x) ≥ g(x) on [a, b], the formula used is A = ∫ dx.
4. The area between curves can sometimes be negative if the lower function is above the upper function.
True
False
5. Determine the area of the region bounded by x = y² and x = y + 2.