I completely understand and I am familiar with double integration and changing the order of integration.
However, it is usually the case that you get an integral of the form:
I=∫ab∫f(x)g(x)f(x,y)dydxi.e. the numerical limits are in the outer integral whilst the variable limits are in the inner integral. This produces a numerical result. Sometimes it is desirable to change the order of integration because of the difficulty involved with integrating the integrand with respect to the inner variable. However, when you make that change of order, you still get an integral which has numerical limits on the outer integral and variable limits on the inner integral - so you get a numerical result either way.
I'm actually tutoring somebody, and one past paper question that has come up in their exam involves an integral where the variable limits are on the outside and the numerical limits are on the inside. I.e.:
I=∫f(x)g(x)∫abf(x,y)dxdyAm I to assume, then, that this is not a mistake and that the answer they want will, indeed, just be a function of
x? Either that or there is another way to deal with this in order to get a numerical result (if so, what?) ... OR the lecturer has simply made an arse of it and it's an erroneous question.