The concept of changing the order of integration evolved to help in handling typical integrals occurring in evaluation of double integrals For example in the given double integral we note that the choice of order of integration is wrong as the inner integration cannot be performe ID: 1031254
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1. Changing the Order of IntegrationThe concept of changing the order of integration evolved to help in handling typical integrals occurring in evaluation of double integrals.For example in the given double integral we note that the choice of order of integration is wrong, as the inner integration cannot be performed. Hence we change the order of integration and try to integrate with respect to x first.On changing the order of integration, the limits of integration change. To find the new limits, we draw the rough sketch of the region of integration. From the sketch, the limits of x and y should determined as usual.MULTIPLE INTEGRALS
2. Sol. Given y = x to y = ∞ and x = 0 to x = ∞ 1. Evaluate by changing the order of integration in
3. 2. Evaluate by changing the order of integration in Sol. Given y = x to y = a and x = 0 to x = a
4. 3. Evaluate by changing the order of integration in Sol.
5. 4. Evaluate by changing the order of integration in Sol. Given y = 0 to y = y2 = 4ax and x = 0 to x = a
6. 5. By changing the order of integration, evaluate Sol. Given y = x2/a to y = 2a – x (i.e.) ay = x2 to x + y = 2a and x = 0 to x = a
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8. Put x2 + y2 = t2 2x dx = 2t dt x dx = t dt6. Evaluate by changing the order of integration in Sol. Given y = x to y = y2 = 2 – x2 (or) x2 + y2 = 2 and x = 0 to x = 1 x2 + y2 = t2When x = 0, t2 = y2 t = yWhen x = y, t2 = 2y2 t = y
9. Put x2 + y2 = t2 2x dx = 2t dt x dx = t dt x2 + y2 = t2When x = 0, t2 = y2 t = yWhen x = , t2 = 2 – y2 + y2 t =
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