Practice question · Put in order
Order the steps for finding the area of the region enclosed between two curves.
- Add the pieces to get the total enclosed area
- Integrate top curve minus bottom curve across each interval
- Solve f(x) = g(x) to find where the curves intersect
- Take the intersection points as the limits of integration
- Decide which curve is the upper one on each interval
Hints
- The limits are not given to you here, they are produced by the curves themselves.
- Which curve is on top must be settled before any subtraction is written down.
Show the answer
- Solve f(x) = g(x) to find where the curves intersect
- Take the intersection points as the limits of integration
- Decide which curve is the upper one on each interval
- Integrate top curve minus bottom curve across each interval
- Add the pieces to get the total enclosed area
Why
Intersections give the limits; the ordering of the curves gives the integrand. Skipping the third step is what produces negative 'areas', and skipping the possibility of a swap is what loses half of a region.
Practise Area Between Curves
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