Final answer:
To calculate the area between two curves, you need to integrate the difference between the curves over a given interval. Follow these step-by-step instructions to find the area.
Step-by-step explanation:
Area Between Two Curves
In calculus, the area between two curves can be found by integrating the difference between the two curves over a given interval. Here are the step-by-step instructions to calculate the area between two curves:
- Identify the equations of the two curves
- Determine the limits of integration (the intersection points of the two curves)
- Subtract the lower curve from the upper curve
- Integrate the resulting expression with respect to x or y depending on the orientation of the curves
- Evaluate the definite integral using the limits of integration
For example, if the two curves are y = x^2 and y = 2x, the area between the curves can be calculated as:
A = ∫[(2x - x^2) dx] from x = 0 to x = 2
Performing the integration and evaluation will give you the desired area.