If [x] is the greatest integer function,then | vedclass

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(D) Let $I = \int_0^5 [x] \, dx$. Since $[x]$ is the greatest integer function,it changes its value at every integer point. We can split the integral

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(D) Let $I = \int_0^5 [x] \, dx$. Since $[x]$ is the greatest integer function,it changes its value at every integer point. We can split the integral as: $I = \int_0^1 [x] \, dx + \int_1^2 [x] \, dx + \int_2^3 [x] \, dx + \int_3^4 [x] \, dx + \int_4^5 [x] \, dx$ $I = \int_0^1 0 \, dx + \int_1^2 1 \, dx + \int_2^3 2 \, dx + \int_3^4 3 \, dx + \int_4^5 4 \, dx$ $I = 0(1-0) + 1(2-1) + 2(3-2) + 3(4-3) + 4(5-4)$ $I = 0 + 1 + 2 + 3 + 4 = 10$.

If $[x]$ is the greatest integer function,then $\int_0^5 [x] \, dx =$

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