if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge?
Solution 1:
Consider $f(x)=\sin(x) / x$.
if $\int_1^{\infty}f(x)\ \mathrm dx$ converges, must $\int_1^{\infty}f(x)\sin x\ \mathrm dx$ converge?
Solution 1:
Consider $f(x)=\sin(x) / x$.