5.6-bo'lim : Aniq integralning ta'rifi
4. \( \displaystyle \int_{6}^{{11}}{{f\left( x \right)\,dx}} = - 7\) berilgan \( \displaystyle \int_{{11}}^{6}{{9f\left( x \right)\,dx}}\) qiymatini aniqlang.
Yechim
Haqiqatan ham bu muammoni ishlatishdan boshqa ko'p narsa yo'q xususiyatlari ushbu bo'limning eslatmalaridan biz berilgan oraliqni qo'lga kiritmagunimizcha, qaysi nuqtada biz berilgan qiymatdan foydalanamiz.
\[\begin{align*}\int_{{11}}^{6}{{9f\left( x \right)\,dx}} & = 9\int_{{11}}^{6}{{f\left( x \right)\,dx}} & \hspace{0.5in}& {\mbox{Property 3}}\\ & = - 9\int_{6}^{{11}}{{f\left( x \right)\,dx}} & \hspace{0.5in} & {\mbox{Property 1}}\\ & = - 9\left( { - 7} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{63}} & & \end{align*}\]