Let f(x)=\min \{[x-1],[x-2], . . .,[x-10]\} where [ {\t}] denotes the greatest integer \leq {\t}. Then \int_0^{10} f(x) {\d} x+\int_0^{10}(f(x))^2 {\d} x+\int_0^{10}|f(x)| {\d} x is equal to ________. [27-Jul-2022-Shift-2]

Definite Integrals Part 2

Section: Mathematics

Question : 18 of 100

Marks: +1, -0

Let f(x)=min{[x−1],[x−2],...,[x−10]} where [t] denotes the greatest integer ≤t. Then

∫

10f(x)dx+

∫

10(f(x))2dx+

∫

10|f(x)|dx is equal to ________.

[27-Jul-2022-Shift-2]

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−f(x),‌	‌ if ‌x≤10
f(x),‌	‌ if ‌x≥10.