絶対値を含む定積分（区間を分ける）（B）

(1) $x\leqq -\dfrac{1}{2}$ で $|2x+1|=-(2x+1)$，$x\geqq-\dfrac{1}{2}$ で $|2x+1|=2x+1$． \[ \int_{-2}^{-\frac{1}{2}}(-2x-1)\,dx+\int_{-\frac{1}{2}}^{1}(2x+1)\,dx=\Bigl[-x^2-x\Bigr]_{-2}^{-\frac{1}{2}}+\Bigl[x^2+x\Bigr]_{-\frac{1}{2}}^{1}=\frac{9}{4}+\frac{9}{4}=\frac{9}{2} \] (2) $0\leqq x\leqq 1$ で $|x^2-1|=1-x^2$，$1\leqq x\leqq 2$ で $|x^2-1|=x^2-1$． \[ \int_0^1(1-x^2)\,dx+\int_1^2(x^2-1)\,dx=\frac{2}{3}+\frac{4}{3}=2 \]