Question

how do i exchange the order of integration for ∫0∞ (∫0y dt) f(y) dy

Answer 1

Do you mean \(\int_0^\infty\left(\int_0^ydt\right)f\left(y\right)dy\) because that's the same, I think, as \(\int_0^\infty yf\left(y\right)dy\) which cannot be simplified IIRC.