In order to find the limits for x, we need the values for which the two functions coincide. We can see from the plot that, to define the bounded region between the two graphs, exp(x) should be the lower limit for y, and 2x+2 should be the upper limit. Title( 'region bounded by y = 2x+2 and y = e^x') It should be large enough to show the region of interest, but small enough so that the region of interest occupies most of

You may need to experiment with the interval to get a useful plot We begin by plotting the two curves on the same axes. For a first example, we will consider the bounded region between The limits we have chosen define the region we intended. While MATLAB cannot do that for us, it can provide some guidance through its graphics and can also confirm that 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

Integrating over Implicitly Defined RegionsĮvaluating a multiple integral involves expressing it as an iterated integral, which can then be evaluated either symbolically.

Integral matlab