Find the Area Between Two Curves: A Step-by-Step Guide for Calculating the Bounded Region

area between 2 curves

(top curve – bottom curve)

The area between two curves refers to the region bounded by two curves on the same coordinate plane. To find the area between two curves, we first need to determine the points at which the curves intersect. We then integrate the difference between the two curves over the interval between the intersection points.

The basic steps for finding the area between two curves are as follows:

1. Identify the two curves and determine their intersection points. We do this by solving the equations of the curves simultaneously.

2. Determine which curve is on top of the other one within the given interval. To do this, we need to compare the y-values of the two curves for each x-value.

3. Set up the integral for the area between the two curves. If the upper curve is y = f(x) and the lower curve is y = g(x), the integral for the area between these curves over the interval [a, b] is:

∫[a,b] (f(x) – g(x)) dx

4. Evaluate the integral using antiderivatives or integration techniques such as u-substitution or integration by parts.

Once we have found the area between the curves, we can interpret it as the area of a region bounded by the two curves. This concept is commonly used in applications such as computing volumes of solids of revolution or calculating areas of cross-sections.

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