Basics
of Multiple Integrals and Applications
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Recall that the total area
under the curve, y = f(x), in Calculus 2 was given by: x2 x2
A = ∫ f(x) dx = ∫ y dx ------------------- (1) x1 x1 The element of area, dA was visualized
as a rectangle of width dx and height y under the
curve y = f(x). The total area then was the “sum” of each
rectangle. The region of integration
extended from x1 to x2 . |
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Next consider the area
between two curves y1 = f1 (x)
and y2 = f2 (x) where the curve for y2
lies above y1 . Using the approach in Calculus 2, the area between
the curves is: x2a A = ∫ (y2 - y1 ) dx ------------------------------------- (2) x1a where x1a and x2a are
the x-coordinates of the points of intersection of the two curves. Click here to
continue with this case. |
Copyright © 2017 Richard C. Coddington
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