Section 16.1 -- Double Integrals over Rectangles

> restart;

> with( plots ):

Warning, the name changecoords has been redefined

> setoptions3d( axes=framed, shading=zhue ):

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Auxiliary Procedures -- execute but do not modify

Example: Example 2 (p. 689)

> f := (64-8*x+y^2)/16;

> xrange := x=0..4;

> yrange := y=0..8;

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The Riemann sum computed on a 2x4 grid of rectangles can be found with

> riemann2( f, xrange, yrange, 2, 4 );

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Taking this example further, note the convergence of the Riemann sums as the number of rectangles increases.

> animate_riemann2( f, xrange, yrange, 6 );

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The (unevaluated) definite integral is

> def_int := Int( Int( f, xrange ), yrange );

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The exact value of this integral is

> value( def_int );

which is approximately

> evalf( % );

Note that the approximating Riemann sums are converging to this value.

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