Final Answer
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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: $\int_a^bf(x)dx=-\int_b^af(x)dx$
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$-\int_{-2}^{0}\left(x-2\right)^2dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (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. We can solve the integral \int\left(x-2\right)^2dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x-2 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Substituting u and dx in the integral and simplify.