Area Between Curves Worksheet
Calculate the area between two curves using integration.
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Area Between Curves Worksheet
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Read each question carefully and calculate the area between the given curves. Show all your work.
1. Find the area of the region bounded by the curves y = x^2 and y = x.
2. Calculate the area enclosed by y = x^2 - 4x and y = -x.
3. To find the area between two curves f(x) and g(x) from x=a to x=b, where f(x) ≥ g(x) on [a,b], you evaluate the definite integral of from a to b.
4. The intersection points of the curves are typically used as the of integration.
5. The area between curves can sometimes be negative if the lower function is subtracted from the upper function.
True
False
6. When finding the area between curves, it is always necessary to graph the functions first.
True
False
7. Determine the area of the region bounded by y = sin(x) and y = cos(x) from x = 0 to x = π/2.
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