How do you evaluate the integral #int dx/(x+2)^(1/3)# from -2 to 4 if it converges?

1 Answer
Andrea S.
Apr 1, 2017

#int_(-2)^4 dx/(x+2)^(1/3) = 3/2root(3)(36)#

Explanation:

The integrand function is continuous in #(-2,4]#, so we can solve the indefinite integral:

#int dx/(x+2)^(1/3) = 3/2(x+2)^(2/3)#

and see that the primitive is continuous also for #x=-2#, so the integral is convergent:

#int_(-2)^4 dx/(x+2)^(1/3) = 3/2[(x+2)^(2/3)]_(-2)^4 = 3/2 6^(2/3) #

#int_(-2)^4 dx/(x+2)^(1/3) = 3/2root(3)(36)#

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