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How do you evaluate the definite integral #int (x-1)^3dx# from [2,3]?

1 Answer

Jan 16, 2018

#int_2^3 (x-1)^3dx = 15/4#

Explanation:

#int_2^3 (x-1)^3dx = int_2^3 (x-1)^3d(x-1)#

#int_2^3 (x-1)^3dx = [(x-1)^4/4]_2^3#

#int_2^3 (x-1)^3dx = (3-1)^4/4 - (2-1)^4/4#

#int_2^3 (x-1)^3dx = (2^4/4-1/4) #

#int_2^3 (x-1)^3dx = (16/4-1/4) =15/4#

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