How would I go about proving convergence of these integrals (not looking for solution just a point in the right direction)?
#Improper Integral Convergence
worn stump
rough trench
main solstice
The improper integral with upper bound infinity is defined as follows:
$\int_{a}^{\infty} f(x) dx = \lim_{b \to \infty} \int_{a}^{b} f(x) dx $
So your first step is to find the definite integral, e.g. for (9) you'd find the value of $ \int_{0}^{b} \sin(x) \sin(x^2) dx$, then take the limit as b goes to infinity.
If the limit exists, the improper integral converges, if it doesn't, it diverges
Hang on seems like latex didn't work let me write it out differently
