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By using intergration by parts, show that the intergral `int_2^4 X( ln X )dx` = `a (ln...
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`U = x^2/2`
`dU = xdx`
`V = lnx`
`dV = 1/xdx`
Using integral by parts;
`intVdU = UV-intUdV`
`int_2^4lnx*xdx = [x^2/2*lnx]_2^4-int_2^4(x^2/2)*1/xdx`
`int_2^4xlnxdx = [x^2/2*lnx]_2^4-int_2^4(x/2)dx`
`int_2^4xlnxdx = [x^2/2*lnx]_2^4-[x^2/4]_2^4`
`int_2^4xlnxdx = (4^2/2xxln4-2^2/2xxln2)-(4^2/4-2^2/4)`
`int_2^4xlnxdx = (16ln2-2ln2)-(4-1)`
`int_2^4xlnxdx = 14ln2-3`
This looks the form of `alnb+c` where;
a = 14
b = 2
c = -3
Posted by jeew-m on July 15, 2013 at 2:03 PM (Answer #1)
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