The discussion centers on evaluating an integral with bounds from negative infinity to zero for an even function, specifically f(y) = f(-y). The user correctly applies the property of integrals, stating that \(\int_a^b f(x) dx = -\int_b^a f(x) dx\), confirming its validity even when the bounds include infinity. By taking the limit to infinity rather than negative infinity, the user successfully concludes their proof, demonstrating a solid understanding of integral properties in calculus.
PREREQUISITESStudents of calculus, mathematicians, and anyone involved in mathematical proofs or analysis of integrals, particularly those dealing with infinite bounds.
\int_a^b f(x) dx = -\int_b^a f(x) dxdmatador said:I am working on a proof in which I have an integral with bounds negative infinity to zero, with an even function, i.e., f(y) = f(-y). I took the limit to infinity rather than negative infinity since y is negative (which is OK I think) but now I have an integral that goes from infinity to 0. What can I make of this? I remember something about this from calculus, but nothing in particular.