- #1
MuIotaTau
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Homework Statement
Rewrite the given sum of iterated integrals as a single iterated integral by reversing the order of integration, and evaluate.
$$\int_0^1 \int_0^x sin x dy dx + \int_1^2 \int_0^{2 - x} sin x dy dx$$
Homework Equations
None
The Attempt at a Solution
I drew the domains of each integral and saw that they appeared different, but I proceeded anyway. Changing the order of integration of each integral, I arrived at
$$\int_0^1 \int_y^1 sin x dx dy + \int_0^1 \int_1^{2-y} sin x dx dy$$
which doesn't appear to help me. This made me further suspicious about how I could possibly combine two integrals over two different domains. Any hints?