defaultwhat is the integral of x^2 from 0 to 2?
Please reason step by step, and put your final answer within oxed{}.
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To find the integral of x^2 with respect to x, we use the power rule of integration, which states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where n is a constant and C is the constant of integration.
So, the integral of x^2 with respect to x is (x^(2+1))/(2+1) + C = (x^3)/3 + C.
Now, we need to evaluate this integral from 0 to 2. We do this by plugging in the limits of integration:
[(2^3)/3 + C] - [(0^3)/3 + C] = (8/3) - (0/3) = 8/3.
So, the integral of x^2 from 0 to 2 is 8/3.
The answer is $\boxed{\frac{8}{3}}$.{
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