View
124
Download
4
Category
Preview:
Citation preview
Integration by Parts
Integration by parts is used when integrating the product of two expressions . We can also sometimes use integration by parts when we want to integrate a function that cannot be split into the product of two things.
Let’s see some examples
u = xdu = dx
dv = cos x dxSdv = Scos x dxv = sin x
More Examples
u = xdu = dx
dv = ex dxSdv = Sex dxv = ex
One More !!!
u = ln xdu = 1/x dx
dv = dxS dv = S dxv = x
Repeated Integration by Parts
u = x2
du = 2x dx dv = e-x dxSdv =S e-x dxv = -e-x
u = xdu = dx
dv = e-x dxSdv =S e-x dxv = -e-x
Integration by Parts for Definite Integrals
Example
t = 1 + x2
dt = 2x dx
½ 2 I I
Recommended