# Difference between revisions of "Science:Math Exam Resources/Courses/MATH200/December 2013/Question 06/Solution 1"

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− | <math> \int_{-1}^{0} \int_{-2}^{2x} e^{y^2}dydx = \int_{-2}^{0} \int_{\frac{y}{2}}^{0} e^{y^2} dxdy | + | <math> \int_{-1}^{0} \int_{-2}^{2x} e^{y^2}dydx = \int_{-2}^{0} \int_{\frac{y}{2}}^{0} e^{y^2} dxdy = \int_{-2}^{0} (xe^{y^2} |_{x = \frac{y}{2}}^{x=0}) dy = \int_{-2}^{0} -\frac{y}{2} e^{y^2}dy \color{red}{=} </math> |

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## Latest revision as of 03:33, 11 November 2017

Like the hint suggests, we need to change the order of integration. First, we must begin by setting up the new bounds. We can begin by drawing the domain of integration.

In order to change the order of integration, we must find the bounds of in terms of and the bounds of in terms of numbers.

We can observe from the picture of the domain of integration that the bounds are equivalent to

Using this, we can change the order of integration.

Let and