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$\int\limits_{-1}^1\{[x]+|x|\} d x$ has the value is : |
0 1/2 1 1/4 |
0 |
$\int\limits_{-1}^1([x]+|x|) d x=\int\limits_{-1}^0(-1-x) d x+\int\limits_0^1(0+x) d x$ $=\left|-x-\frac{x^2}{2}\right|_{-1}^0+\left|\frac{x^2}{2}\right|_0^1=0-\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-0\right)=0$ Hence (1) is the correct answer. |
