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# Integration by parts: definite integrals

AP.CALC:
FUN‑6 (EU)
,
FUN‑6.E (LO)
,
FUN‑6.E.1 (EK)
When finding a definite integral using integration by parts, we should first find the antiderivative (as we do with indefinite integrals), but then we should also evaluate the antiderivative at the boundaries and subtract.

## Want to join the conversation?

• Does it still work if we chose to assign x to f(x) or g(x) to make it more complicated?
• Yes, but the point is to use the easier way.
• Any general rules to know straight away when to use Integration by parts and when to use u-substitution? Thanks.
• Integration by parts tends to be more useful when you are trying to integrate an expression whose factors are different types of functions (e.g. sin(x)*e^x or x^2*cos(x)).

U-substitution is often better when you have compositions of functions (e.g. cos(x)*e^(sin(x)) or cos(x)/(sin(x)^2+1)).