Area Between Curves

Calculus 1 · Axiom Academy

Finding the area trapped between the line y = x and the parabola y = x^2 Find the area of the region enclosed by the line y = x and the parabola y = x^2 between their two points of intersection. On the line sits above the parabola, so each thin vertical strip has height x - x^2 . Nice work — you found the area between two curves from start to finish. The recipe was: Find the intersections: set the functions equal, x = x^2 , to get the bounds x = 0 and x = 1 . Identify top and bottom: on the line y = x lies above the parabola y = x^2 . The same three steps work for any two curves — just find where they cross, subtract the lower function from the upper one, and integrate across the interval.

This is the written version of the interactive lesson above. See the full Calculus 1 course.