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.

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

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

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