Practice Area Between Curves in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The area of the region enclosed between two functions f(x) and g(x) from x = a to x = b, computed as A = \int_a^b |f(x) - g(x)|\,dx.
To find the area between two curves, subtract the lower curve from the upper curve and integrate. It's like finding the area under the top curve and subtracting the area under the bottom curve—the difference is the area of the 'sandwich' between them.
Example 1
easyFind the area between f(x) = x+2 and g(x) = x^2 from x=-1 to x=2.
Example 2
hardFind the total area enclosed between y = x^3 - x and the x-axis.
Example 3
easyFind the area between y = 4-x^2 and the x-axis where the parabola is above the axis.
Example 4
mediumFind the area between y = x^2 and y = 2x.