Changing
Order of Integration for a Double Integral
Example: Reverse the order of integration for the integral shown below. 2 ln x I = ∫ ∫ f(x,y) dy dx 1 0 |
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The limits of integration are y = 0 to y = ln x and x = 1 to x = 2.
Integration in the x-direction: ey ≤ x ≤ 2 Integration in the y-direction: 0 ≤ y ≤ ln 2 y = ln 2 x = 2 So I = ∫ ∫ f(x,y) dx dy (result) y = 0 x = ey |
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