Монгол Бодлогын Сан

Заавар: $f(x)$ функцийн эх функц нь $F(x)$ бол $$\int_{a}^{b}f(x)\,\mathrm{d}x=F(b)-F(a)$$ байна.

Бодолт: $$\int\frac{\,\mathrm{d}x}{(11+5x)^3}=\dfrac{1}{5}\int(11+5x)^{-3}\mathrm{d}(11+5x)=-\dfrac{1}{10}(11+5x)^{-2}+C$$ тул $$\displaystyle\int_{-2}^{-1}\frac{\,\mathrm{d}x}{(11+5x)^3}=-\dfrac{1}{10(11+5x)^2}\bigg|_{-2}^{-1}=$$ $$=-\dfrac{1}{10(11+5\cdot(-1))^2}+\dfrac{1}{10(11+5\cdot(-2))^2}=$$ $$=-\dfrac{1}{360}+\dfrac{1}{10}=\dfrac{35}{360}=\dfrac{7}{72}$$