Area Between Curves Worksheet
Grade 12 Calculus worksheet focusing on calculating the 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. 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 = x + 2.
2. Calculate the area enclosed by the graphs of y = sin(x) and y = cos(x) from x = π/4 to x = 5π/4.
3. Which integral represents the area of the region bounded by y = x³ and y = x?
∫(-1 to 1) (x - x³) dx
∫(-1 to 0) (x³ - x) dx + ∫(0 to 1) (x - x³) dx
∫(-1 to 1) (x³ - x) dx
∫(0 to 1) (x³ - x) dx
4. Determine the area of the region bounded by x = y² and x = 4.
5. The area between two curves f(x) and g(x) from a to b is always given by ∫(a to b) [f(x) - g(x)] dx, regardless of which function is greater.
True
False