33 - double integrals.pdf - 33 Double integrals Recall we developed the integral of function y=f(x of a single variable to determine the area between

33 - double integrals.pdf - 33 Double integrals Recall we...

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1 33 Double integrals Recall we developed the integral of function y=f(x)of a single variable to determine the area between the graph of a function and the x-axis (i.e. area under the curve): We began by approximating the region by a collection of rectangles. The total area is a Riemann sum.
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3 We will focus on integrals over rectangular domains: For a function A tower constructed over a rectangular domain Has volume (base)(width)(height): With The Riemann sum over a collection of rectangles is a double sum: axb, cydz=f(x, y)Δxi=xi+1-xinXi=0mXj=0f(xi, yj)ΔxiΔyjΔyj=yj+1-yj[xi, xi+1][yj, yj+1](xi+1-xi)·(yj+1-yj)·f(xi, yj)
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