Question

By reversing the order of integration, evaluate
\[\int\limits_0^\infty g(u)e^{-su}\text du\] where; \[g(t)=\int\limits_0^t e^x\sin(2(t-x))\text dx\]

Answer 1

\[\int\limits_0^\infty \int\limits_0^u e^x\sin(2(u-x))\text dxe^{-su}\text du\]

Answer 2

im not sure what the new limits will be

Answer 3

the book im using suggest to draw a picture to help find the new limits but im not sure what to draw,