Opamp applications with capacitors:
##Integrator
\(i_R = i_C\)
\(i_R = V_i/R\)
\(i_C = -C d v_o /dt\)
\(dv_o = -\frac{1}{RC}v_idt\)
Integrating both sides:
\(v_o = -\frac{1}{RC} \int_0^tv_i(t) dt\)
\(i_R = i_C\)
\(i_R = - V_o/R\)
\(i_C = -C d v_i /dt\)
\(v_o = -RC dv_i(t)/dt\)