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How do you test the improper integral #int(x-1)^(-2/3)dx# from #[0,1]# and evaluate if possible?

1 Answer

Aug 5, 2017

Please see below.

Explanation:

#int_0^1 (x-1)^(-2/3) dx = lim_(brarr1^-)int_0^b (x-1)^(-2/3) dx#

Integrate by substitution #u = x-1# to get

# = lim_(brarr1^-)3[root(3)(x-1)]_0^b#

# = lim_(brarr1^-)3(root(3)(b-1)-root(3)(-1))#

# = 3(0-(-1)) = 3#

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