Монгол Бодлогын Сан

Заавар: Модулийн тодорхойлолт болон интегралын аддитив чанар ашиглан бод. $$\int_a^b f(x)\,\mathrm{d}x=\int_a^c f(x)\,\mathrm{d}x+\int_c^b f(x)\,\mathrm{d}x$$

Бодолт: $$|5x-3|=\left\{ \begin{array}{rl} 5x-3, & x\ge 0.6\\ -(5x-3), & x<0.6 \end{array} \right.$$ тул $$\begin{align*} \int_{-2}^1|5x-3|\,\mathrm{d}x&=\int_{-2}^{0.6}|5x-3|\,\mathrm{d}x+\int_{0.6}^1|5x-3|\,\mathrm{d}x=\\ &=-\int_{-2}^{0.6}(5x-3)\,\mathrm{d}x+\int_{0.6}^1(5x-3)\,\mathrm{d}x=\\ &=-\left(\dfrac{5x^2}{2}-3x\right)\Bigg|_{-2}^{0.6}+\left(\dfrac{5x^2}{2}-3x\right)\Bigg|_{0.6}^{1}=\\ &=-\left(\dfrac{5\cdot 0.6^2}{2}-3\cdot0.6\right)+\left(\dfrac{5\cdot (-2)^2}{2}-3\cdot(-2)\right)+\\ &{~~~~~~~}+\left(\dfrac{5\cdot 1^2}{2}-3\cdot1\right)-\left(\dfrac{5\cdot 0.6^2}{2}-3\cdot0.6\right)=\\ &=-(0.9-1.8)+(10+6)+(2.5-3)-(0.9-1.8)=17.3 \end{align*}$$