![]() ![]() We will now address the problem of determining limits for a double integral from a geometric description of the region of However, we can evaluate the integral numerically, using double.ĭouble(int(int(exp(x^2-y^2),y,1-x,1-x^2),x,0,1)) Warning: Explicit integral could not be found. In terms of erf(x), which is the (renormalized) antiderivative of exp(-x^2). However, if we change the integrand to, say,Įxp(x^2 - y^2), then MATLAB will be unable to evaluate the integral symbolically, although it can express the result of the first integration 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.Įxample 1 We evaluate the iterated integral ![]()
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