Difference between revisions of "Integration By Parts"
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====[[Integration By Parts]]==== | ====[[Integration By Parts]]==== | ||
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#Performing Integration By Parts <math>\int f(x) g'(x) \,dx = f(x)g(x) - \int f'(x) g(x) \,dx </math> | #Performing Integration By Parts <math>\int f(x) g'(x) \,dx = f(x)g(x) - \int f'(x) g(x) \,dx </math> | ||
#Performing Integration By Parts <math>\int u \,dv = uv - \int v \,du</math> | #Performing Integration By Parts <math>\int u \,dv = uv - \int v \,du</math> | ||
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====Explaining==== | ====Explaining==== | ||
When you are looking at this equation | When you are looking at this equation | ||
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for example if we say u is f(x) than du is derivative of f(x) so it will be f'(x). | for example if we say u is f(x) than du is derivative of f(x) so it will be f'(x). | ||
<math>\int u \,dv = uv - \int v \,du</math> | |||
can be think as | |||
<math>\int f(x) \,g'(x) = (f(x) * g(x)) - \int g(x) \, f'(x)</math> | |||
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Latest revision as of 06:16, 17 September 2021
Integration By Parts
- Performing Integration By Parts
- Performing Integration By Parts
Explaining
When you are looking at this equation
you may have been confused by u,du,v,dv
you can just under stand it as
- u = f(x)
- du = f'(x)
- v = g(x)
- dv = g'(x)
so by looking at u and v as a function we you say du or dv is derivative of that function.
for example if we say u is f(x) than du is derivative of f(x) so it will be f'(x).
can be think as
