3) Why is it advantageous to switch the order of integration (and therefore the

Question

3) Why is it advantageous to switch the order of integration (and therefore the limits) in Example 7? (6, 2) Figure 16.19: The region of integration for Example 6, showing the vertical strip mple7 Evaluate Vy+1 dy dx using the region sketched in Figure 16.19 Since v y3 +1 has no elementary antiderivative, we cannot calculate the inner integral symboli- cally. We try reversing the order of integration. From Figure 16.19, we see that horizontal strips go from x = 0 to x = 3y and that there is a strip for every y from 0 to 2. Thus, when we change the order of integration we get ion 0 J0 Now we can at least do the inner integral because we know the antiderivative of z. What about the outer integral? (31)/2 dy Jo Jo = (y3 + 1)3/21-27-1 = 26 Thus, reversing the order of integration made the integral in the previous problem much easier Notice that to reverse the order it is essential first to sketch the region over which the integration is being performed.

Explanation / Answer

Sometimes we cant able to integrate with the normal integration,

hence we will change the order of integration which will make outer label as 'y' and inner label 'x'

then it will reduce the complexity of solving the problem by making one variable dependent on other.

hence reversing the order of integration would make our calculation easier.

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