# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

Learn how to solve definite integrals problems step by step online.

$-\int_{-2}^{0}\left(x-2\right)^2dx$

Learn how to solve definite integrals problems step by step online. Integrate (x-2)^2 from 0 to -2. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. 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. Simplifying. Evaluate the definite integral.

$-\frac{56}{3}$$\,\,\left(\approx -18.666666666666664\right)$

### Problem Analysis

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

### Main topic:

Definite integrals

~ 1.29 seconds