How do you evaluate the definite integral #int (x-2) dx# from #[-1,0]#?

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Answer 1 · 2018-03-25T16:19:34

#-5/2#

#int_-1^0(x-2)dx#

Using the power formula for integral computation, increase the exponent on the variable and divide each term by its new exponent.

#[x^2/2-(2x^1)/1]_-1^0#

#[x^2/2-2x]_-1^0#

Now plug in the upper and lower bounds of integration as values for x and subtract.

#[((0)^2/2-2(0))-((-1)^2/2-2(-1))]#

#[(0-0)-(1/2+2)]=-5/2#