Topic Category: Change of Order

Change of Order-7

Example 1 : Change of order of integration in double integral Solution : Let the compare the given integral to the integral in standard form The bounding curves are given by Let us plot these curves to get the region of integration After changing the order, the integral will be of the form To get …

Change of Order-6

Example 1 : Evaluate over the region enclosed by and . Solution : The region of integration is shown in the figure Example 2 : Evaluate the integral over the region bounded by the lines y = x, y = x – 1, y = 0 and y = 1. Solution : The region of …

Change of Order-5

Example 1 : Evaluate over the region bounded by . Solution : The region of integration is bounded by and The region of integration is shown in figure

Change of Order-4

Example 1 : Change the order of integration. Solution : The given integral is Comparing the two integrals, the curves bounding the region of integration are given by Let us trace all the curves to get region of integration After changing the order of integration, the integral changes to The domain has to be partitioned …

Change of Order-3

Example 1 : Change the order of double integration Solution : The given integral is Comparing the two integral, the curves bounding the region of integration are given by & are the part of ellipse The region of integration is shown in figure After changing the order, the given integral converts to To get the …

Change of Order-2

Example 1 : Change the order of integration in Solution : On comparing the limits of integral is given form to its standard form The bounding curves are given by Let us plot all these curves The domain of integration is the region bounded by all the four bounding curves as shown in figure.The arrow …

Change of Order-1

Let us take the following example : Theorem 1 : Change the order of integration in where f is a function of x and y. Solution : Step 1 : The first step involves getting the bounding curves of domain of integration. Let us compare the limits of given integral to its standard form comparing …