Can you explain to me the difference between to give up and to give in?

( I have consulted several dictionaries and I understand that the structure is different and they can´t be used interchangeably. But some cases puzzled me.)

E.g: I did my best to do the math test, but it was impossible as it was too hard. So, I gave in. ( Is this correct? I understand to give in as the same as "to accept sth even though you´re reluctant to", but in this case, can you say the that you accepted your defeat, as long as the ficculty of the test overcame you?)

Thanks,

Andréa.