COLLEGE CALCULUS. HELP!
posted by LILY on .
Evaluate the definite integral
∫(0,2) (x1)^25 dx..
thats how i got stuck
u=x1, then du=dx
=∫(0,2) u^25du
=(1/26)u^26. i don't know what to do with integral (2,0)..

just keep working away. You have the correct answer
1/26 (x1)^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 xintercept 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 ∫(x1)^25 dx from 0 to 1
= (1/26)(x1)^26  from 0 to 1
= 0  (1/26)(1)^26 = 1/26
and
∫(x1)^25 dx from 1 to 2
= (1/26)(x1)^26  from 1 to 2
= (1/26)(1)^26  (1/26)(0) = 1/26
so the total integral is 2/26 or 1/13