is the integration of
(x-2)^2
= 1/3(x-2)^3
Yes, that is correct.
In order to determine if the integration of (x-2)^2 is equal to 1/3(x-2)^3, we can follow these steps:
Step 1: Determine the indefinite integral of (x-2)^2.
To integrate (x-2)^2, we can use the power rule of integration. According to the power rule, the integral of x^n is (1/(n+1))x^(n+1), where n is any real number except for -1. Applying the power rule, we get:
∫(x-2)^2 dx = (1/3)(x-2)^(2+1) + C
= (1/3)(x-2)^3 + C
Where C is the constant of integration.
Step 2: Compare the result with 1/3(x-2)^3.
Comparing the result we obtained from integration, (1/3)(x-2)^3 + C, with 1/3(x-2)^3, we can see that they are indeed equal. Therefore, the integration of (x-2)^2 is equal to 1/3(x-2)^3.