5.6-bo'lim : Aniq integralning ta'rifi
6. \( \displaystyle \int_{5}^{2}{{f\left( x \right)\,dx}} = 3\) va \( \displaystyle \int_{5}^{9}{{f\left( x \right)\,dx}} = 8\) berilgan \( \displaystyle \int_{2}^{9}{{f\left( x \right)\,dx}}\) qiymatini aniqlang.
Yechim
Avval biz foydalanishimiz kerak Mulk 5 ushbu bo'limning eslatmalaridan integralni muammo bayonotida berilgan integrallar bilan bir xil chegaralardan foydalanadigan ikkita integralga ajratish.
E'tibor bering, biz ushbu nuqtada limitlar to'g'ri joydami yoki yo'qmi, deb tashvishlanmaymiz.
\[\int_{2}^{9}{{f\left( x \right)\,dx}} = \int_{2}^{5}{{f\left( x \right)\,dx}} + \int_{5}^{9}{{f\left( x \right)\,dx}}\]2-qadam
Nihoyat, biz qilishimiz kerak bo'lgan yagona narsa foydalanishdir Mulk 1 Ushbu bo'limning eslatmalaridan birinchi integralning chegaralarini o'zgartiring, shunda ular berilgan integralning chegaralari bilan mos keladi. Keyin berilgan qiymatlardan integralning qiymatini aniqlash uchun foydalanishimiz mumkin.
\[\int_{2}^{9}{{f\left( x \right)\,dx}} = - \int_{5}^{2}{{f\left( x \right)\,dx}} + \int_{5}^{9}{{f\left( x \right)\,dx}} = - \left( 3 \right) + 8 = \require{bbox} \bbox[2pt,border:1px solid black]{5}\]