Finding areas between curves
Explore the area under the line and the area under the quadratic. Then look at both at the same time to see how to find the area between two curves.
Will this technique work to find the area between any two curves?
What if one of the curves is below the x-axis, will this technique still work?
How will you find the limits of integration for the two functions?
Summary of area between two curves
We know that the area is the quantity which is used to express the
region occupied by the two-dimensional shapes in the planar lamina. In
calculus, the evaluate the area between two curves, it is necessary to
determine the difference of definite integrals of a function. The area
between the two curves or function is defined as the definite integral
of one function (say f(x)) minus the definite integral of other
functions (say g(x)). Thus, it can be represented as the following:
Area between two curves = ∫ab [f(x)-g(x)]dx