the resistor is not "required" for discharging - and the value of that resistor is not critical. In some cases it is just an equivalent for the on-resistance of the switch.
The only restriction is the following: The time constant T=Rswitch*C must be small (at least factor of 10...20) against the time you can spend to discharge the capacitor. That's all.
It's not exactly required for discharge. But without it, the switch contacts may be possibly welded or at least excessively weared with higher capacitance values. Using an electronic switch, it's internal resistance is mostly sufficient.
I tried to wire integrator circuit with and without resistance and I found that with resistance, the circuit works fine(about 1K) and resistor less than 500 ohms, my output goes to zero even with base open. Without resistance, the output is always zero. Could you explain that...
[Not at all. What's the involved reset switch? Are you sure, it's open during integrate?]
Reset switch is transistor. Yes it is open during integration.
Why don't you show us the complete circuitry?
If you know the purpose of the discharging switch you also should know what can - and in nearly all cases will - happen if the switch is open. OK?
Additional question: What is the integrating time constant - and how long is your integrating period?