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

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Answer 1 · 2016-11-03T19:20:16

I found: $int_-2^3(-2x+2)dx=5$

We can write the integral as:

$int-2xdx+int2dx=-2intxdx+2intdx=$

we can now integrate to get:

$=-2x^2/2+2x=-x^2+2x$

we now substitute the exteremes of integration into our result and subtract:

for $x=3$ we get:: $-9+6=-3$

for $x=-2$ we get: $-4-4=-8$

Let us subtract them:
$-3-(-8)=5$
so finally:

$int_-2^3(-2x+2)dx=5$

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