5.6-bo'lim : Aniq integralning ta'rifi
7. \( \displaystyle \int_{{ - 4}}^{0}{{f\left( x \right)\,dx}} = - 2\), \( \displaystyle \int_{{31}}^{0}{{f\left( x \right)\,dx}} = 19\) va \( \displaystyle \int_{{20}}^{{31}}{{f\left( x \right)\,dx}} = - 21\) berilgan \( \displaystyle \int_{{ - 4}}^{{20}}{{f\left( x \right)\,dx}}\) qiymatini aniqlang.
Yechim
Avval biz foydalanishimiz kerak Mulk 5 ushbu bo'limning eslatmalaridan integralni muammo bayonotida berilgan integrallar bilan bir xil chegaralardan foydalanadigan uchta integralga ajratish.
E'tibor bering, biz ushbu nuqtada limitlar to'g'ri joydami yoki yo'qmi, deb tashvishlanmaymiz.
\[\int_{{ - 4}}^{{20}}{{f\left( x \right)\,dx}} = \int_{{ - 4}}^{0}{{f\left( x \right)\,dx}} + \int_{0}^{{31}}{{f\left( x \right)\,dx}} + \int_{{31}}^{{20}}{{f\left( x \right)\,dx}}\]2-qadam
Nihoyat, biz qilishimiz kerak bo'lgan yagona narsa foydalanishdir Mulk 1 Ushbu bo'limning eslatmalaridan ikkinchi va uchinchi integrallarning chegaralarini almashtiring, shunda ular berilgan integralning chegaralari bilan mos keladi. Keyin berilgan qiymatlardan integralning qiymatini aniqlash uchun foydalanishimiz mumkin.
\[\int_{{ - 4}}^{{20}}{{f\left( x \right)\,dx}} = \int_{{ - 4}}^{0}{{f\left( x \right)\,dx}} - \int_{{31}}^{0}{{f\left( x \right)\,dx}} - \int_{{20}}^{{31}}{{f\left( x \right)\,dx}} = - 2 - \left( {19} \right) - \left( { - 21} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{0}\]