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Integral Calculus question (Integration by parts)?
My question is why do we have to solve for ∫f(x)g'(x)dx?
Ok
d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
∫[d/dx[f(x)g(x)]]=∫[f'(x)g(x)]+∫[f(x)g'(x)]
f(x)g(x)= ∫[f'(x)g(x)]+∫[f(x)g'(x)] here is my question why do we have to solve for ∫[f(x)g'(x)] instead ∫[f'(x)g(x)]. is it the same thing?
1 Answer
- davidLv 77 years agoFavorite Answer
Yes .. they are the same thing. You control which function is called f(x) and which is called g(x) and since they are a product ... ab = ba so the 1st function does NOT have to be f(x) it could be g(x). The real determination is which function will make the integration easier.
