- #1

pmqable

- 13

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the definite integral is: integral from 0 to 1 of ln(x). i used integration by parts (u=ln(x), du=1/x dx, dv=dx, v=x) to show that the integral is equal to:

[x*ln(x)] (1,0) - integral from 0 to 1 of dx.

this gives 1*ln(1)-0*ln(0)-(1-0)

ln(1)=0, so the equation is now

0*ln(0)-1

0*ln(0) is an indeterminate form, so i used the limit:

lim x-->0 x*ln(x)

lim x-->0 ln(x)/(1/x)

lim x-->0 (1/x)/(-1/x^2)

lim x-->0 -x

=0.

so the area is 0-1=-1, which doesn't make sense. what did i do wrong?

[x*ln(x)] (1,0) - integral from 0 to 1 of dx.

this gives 1*ln(1)-0*ln(0)-(1-0)

ln(1)=0, so the equation is now

0*ln(0)-1

0*ln(0) is an indeterminate form, so i used the limit:

lim x-->0 x*ln(x)

lim x-->0 ln(x)/(1/x)

lim x-->0 (1/x)/(-1/x^2)

lim x-->0 -x

=0.

so the area is 0-1=-1, which doesn't make sense. what did i do wrong?

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