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(A) Let $I = \int_0^8 [x] dx$. Since $[x]$ is the greatest integer function,it takes constant integer values on intervals $[n, n+1)$. We can split the

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$28$

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(A) Let $I = \int_0^8 [x] dx$. Since $[x]$ is the greatest integer function,it takes constant integer values on intervals $[n, n+1)$. We can split the integral as: $I = \int_0^1 0 dx + \int_1^2 1 dx + \int_2^3 2 dx + \int_3^4 3 dx + \int_4^5 4 dx + \int_5^6 5 dx + \int_6^7 6 dx + \int_7^8 7 dx$. Evaluating each integral: $I = 0 + 1(2-1) + 2(3-2) + 3(4-3) + 4(5-4) + 5(6-5) + 6(7-6) + 7(8-7)$. $I = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7$. $I = \frac{7(7+1)}{2} = \frac{7 	imes 8}{2} = 28$.

If $[x]$ is the greatest integer function not greater than $x$,then $\int_0^8 [x] dx$ is equal to

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