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Step-by-step Solution

Integrate (x-2)^2 from 0 to -2

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Answer

$\frac{56}{3}i$

Step-by-step explanation

Problem to solve:

$\int_0^{-2}\left(\left(x-2\right)^2\right)dx$
1

Apply the formula: $\int\left(x+a\right)^ndx$$=\frac{\left(x+a\right)^{\left(n+1\right)}}{n+1}$, where $a=-2$ and $n=2$

$\left[\frac{\left(x-2\right)^{3}}{3}\right]_{0}^{-2}$
2

Evaluate the definite integral

$\frac{\left(-2-2\right)^{3}}{3}-1\left(\frac{\left(0-2\right)^{3}}{3}\right)$

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Answer

$\frac{56}{3}i$
$\int_0^{-2}\left(\left(x-2\right)^2\right)dx$

Main topic:

Integration by substitution

Used formulas:

4. See formulas

Time to solve it:

~ 0.87 seconds