Монгол Бодлогын Сан

Заавар: $$\int_a^bf(x)dx=\int_a^cf(x)dx+\int_c^bf(x)dx$$ ашиглан модулиас гаргаж бод.

Бодолт: $$\begin{align*} \int_{0}^4 |x-2|\,\,\mathrm{d}x&=\int_{0}^2 |x-2|\,\,\mathrm{d}x+\int_{2}^4 |x-2|\,\,\mathrm{d}x\\ &=\int_0^2-(x-2)dx+\int_2^4 (x-2)dx\\ &=-\int_0^2(x-2)dx+\int_2^4 (x-2)dx\\ &=-\dfrac{(x-2)^2}{2}\Bigg|_0^2+\dfrac{(x-2)^2}{2}\Bigg|_2^4\\ &=-(0-2)+(2-0)=4 \end{align*}$$