We begin by plotting the two curves on the same axes. For a first example, we will consider the bounded region between the curves y = 2x+2 and y = exp(x). While MATLAB cannot do that for us, it can provide some guidance through its graphics and can also confirm that the limits we have chosen define the region we intended. We will now address the problem of determining limits for a double integral from a geometric description of the region of integration. However, we can evaluate the integral numerically, using double. Warning: Explicit integral could not be found. However, if we change the integrand to, say, exp(x^2 - y^2), then MATLAB will be unable to evaluate the integral symbolically, although it can express the result of the first integration in terms of erf(x), which is the (renormalized) antiderivative of exp(-x^2). There is, of course, no need to evaluate such a simple integral numerically. We can even perform the two integrations in a single step: int(int(x*y,y,1-x,1-x^2),x,0,1) To evaluate the integral symbolically, we can proceed in two stages. ![]() We begin by discussing the evaluation of iterated integrals. ![]() Integrating over Implicitly Defined RegionsĮvaluating a multiple integral involves expressing it as an iterated integral, which can then be evaluated either symbolically or numerically.
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