Area Under a Curve

Find areas between curves and volumes of revolution using definite integrals, with limits of integration and the top-minus-bottom setup shown. Try “area between y = x² and y = 2x”.

Try an example:

How the Area Under a Curve works

  1. Find where the curves intersect to get the limits (x = 0 and x = 2).
  2. Set up the integral of (top − bottom) between the limits.
  3. Integrate and evaluate to get the area (4/3).

Frequently asked questions

How do I find the limits of integration?

Set the two functions equal and solve for x; the solutions are your intersection points.

What is the disc method?

It finds volume of revolution: V = π∫[f(x)]² dx about the x-axis.

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