How to Find the Area Between Two Curves?
To calculate the area between two curves, use the following steps:
- Step 1: Determine the points of intersection between the two curves by substituting value of one variable from one curve to another curve.
- Step 2: Decide which curve has higher values in between the points of intersections if there are more than two points of intersection then check this for each possible interval.
- Step 3: Set up the integral for the area between the two curves using the difference of both curves.
- Step 4: Evaluate the integral using integration techniques such as u-substitution or integration by parts.
Thus, the area between two curves is calculated.
If both the curves are defined as x1 = f(y) and x2 = g(y) and all the other assumptions remain the same as above, then the area between them is given as
[Tex]\bold{A = \int^{b}_a[f(y) â g(y)]dy} [/Tex]
Where,
- a and b are the limits of integration, which are the y-values where the curves intersect
- A is the area between both curves
Area Between Two Curves: Formula, Definition and Examples
Area Between Two Curves in Calculus is one of the applications of Integration. It helps us calculate the area bounded between two or more curves using the integration. As we know Integration in calculus is defined as the continuous summation of very small units. The topic âArea Between Two Curvesâ has applications in the various fields of engineering, physics, and economics.
Area Between Two Curves: Formula, Definition and Examples
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