I'm trying to use Excel to calculate Fourier coefficients. But I'm confused on which method should be used to used to approximate $$\int f(x)\cos(x)dx$$ and $$\int f(x)\sin(x)dx $$.
$1.\quad$ trapezoid $\cos(x)$ & trapezoid $\sin(x)$
$2.\quad$ trapezoid definite integral $\cos(x)dx$ & trapezoid definite integral $\sin(x)dx$
I found an example excel sheet (https://quickfield.com/harmonics_analysis_excel.htm) that seems to takes the definite integral of the cosine & sine term.
Is this a more accurate method than averaging $f(x)\cos(x)$ and $f(x)\sin(x)$ normally?