Question

a double integeration question double integral over limit 1 to and limit 1 to x dydx upon x2 + y2

Answer 1

You do a partial integration of the Internal integration, then the same on the external.
eg,
\[\int\limits_{5}^{y}\int\limits_{3}^{x}(x+y)dxdy\]
Would start with you doing:
\[\int\limits_{3}^{x}(x+y)dx\]
With respect to x, so you pretend y is just a number (a constant).

Then do what's left.

Answer 2

\[\int\limits_{1}^{2}\int\limits_{1}^{x} dydx/x^2+y^2\] is the question how to solve

Answer 3

It'll look nicer if you make it:
\[\int\limits_{1}^{2}\int\limits_{1}^{x} 1/(x ^{2}+y ^{2}) dydx\]

Do the internal part first:
\[\int\limits_{1}^{x}1/(x ^{2}+y ^{2}) dy\]

Do the integration, which doesn't look too easier, but try substitution. Treat x like a constant, and when you enter your limits you'll be left with all x's. Then do the second integration which''ll be easier.