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I have faced the following question. In our lab we perform different measurements on Transistors. We program a scope and that controls the tests. For one of our tests we would like to calculate the total charge Q. Mathematically this is given by

Q=∫ dt i(t), where i(t) is given by i(t) = v(t)/R, i(t)= current, v(t)=voltage, R= resistivity ( constant value), for a time interval [t1, t2]

We cannot measure i(t) directly but we can measure v(t). This means

Q=∫dt v(t)/R.

We have noticed the following

1. if we define Q1 = ∫dt ( v(t)/R)

2. or if we define Q2= (∫dt v(t))/R

Mathematically these two integrals should produce the same result. But we see completely different results. I wonder if this depends on the numerical methods used in integration or has another reason.

Thank you for your help.

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# Numerical intergration of a set of measured data points

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