Question

A 5v, 1khz sinusoidal signal is applied to the input of an op amp integrator, R = 100k C = 1uF determine the Vout

Answer 1

If you assume Vin = 5 sin(2 pi 1K t) then
Vout = - (5/(2 pi 1K) cos(2 pi 1K t)
it would be just the integral as long a RC >> then the period

Answer 2

This is the o/p of an op-amp integrator
\[Vout = -\frac{ 1 }{ RC }\int\limits_{0}^{t}Vin dt\]
Substitute the values of R, C and Vin (5sin(2*pi*1000))