What is the antiderivative of (t - 2)dt from x to 3x?

Question

I started with a u substitution and got u = 3x and du = 3 dx. I wasn't sure how to handle the lower bound of "x".

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Answer 1 · 2018-04-13T14:22:35

# 4x(x-1)#.

By the Fundamental Theorem of Calculus, we have,

#int_x^(3x) (t-2)dt#,

#=[t^2/2-2t]_x^(3x)#,

#=[{(3x)^2/2-2(3x)}-{x^2/2-2x}]#,

#={(9x^2)/2-6x}-{x^2/2-2x}#,

#=4x^2-4x#,

#=4x(x-1)#.