The integral 2∫cos(kx)dk from 0 to infinity is classified as an improper integral, which does not converge. To evaluate such integrals, one must use limits instead of directly substituting infinity. Specifically, the limit lim_k->∞ sin(kx)/x is considered, but it does not exist due to the oscillatory nature of the sine function. This discussion highlights the importance of understanding improper integrals and the behavior of oscillating functions in calculus.
PREREQUISITESStudents and professionals in mathematics, particularly those studying calculus, as well as educators looking to enhance their understanding of improper integrals and oscillatory behavior in functions.
Like this? ##2\int_0^{\infty}\cos(kx) dk##maverick_76 said:okay so I have this integral:
2∫cos(kx)dk
The bounds are from zero to infinity, this doesn't converge but is there any other way to describe this?
The limit doesn't exist because sin(kx) oscillates endlessly.maverick_76 said:okay so the limit would be lim_k->∞ sin(kx)
xHow would I go about evaluating it? Is there a substitution trick?