Posted by LILY on Saturday, April 14, 2012 at 3:07am.
just keep working away. You have the correct answer
1/26 (x-1)^26 [0,2]
= 1/26 [(1)^26 - (-1)^26]
= 1/26 [1 - 1]
= 0
you have to break up your integral into two parts, since there is an x-intercept in your domain from 0 to 2, namely x = 1
think of it as finding the area from x=0 to x=1 plus the area from x=1 to x=2
we get ∫-(x-1)^25 dx from 0 to 1
= (-1/26)(x-1)^26 | from 0 to 1
= 0 - (-1/26)(-1)^26 = 1/26
and
∫(x-1)^25 dx from 1 to 2
= (1/26)(x-1)^26 | from 1 to 2
= (1/26)(1)^26 - (1/26)(0) = 1/26
so the total integral is 2/26 or 1/13
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