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The value of $\int_{-1}^{15}sgn(\{x\})dx$, where {*} denotes the fractional part function, is |
8 16 24 0 |
16 |
$\int_{-1}^{15}sgn(\{x\})dx=\int_0^{16}sgn(\{x-1\})dx$ (by property) $=\int_{-1}^{16}sgn(\{x\})dx=16\int_0^1sgn(\{x\})dx$ $=16\int_0^1sgn(x)dx=16\int_0^11.dx=16$ |
