Determine whether the integral is convergent or divergent. infinity 85 cos(pi t) dt negative infinity

Question

Is it divergent?

Answer 1

∫_{(from -∞ to ∞)}85cos(πt)dt = 2∫_{(from 0 to ∞)}85cos(πt)dt  (by symmetry)

 

                                     = 170lim_b→∞[∫_{(from 0 to b)}cos(πt)dt]

 

                                     = (170/π)lim_b→∞[sin(πb) - sin0]

 

                                     = (170/π)(lim_b→∞sin(πb))

 

Since lim_b→∞sin(πb) does not exist (because sin(πb) oscillates between -1 and 1 forever), the given integral is DIVERGENT.