_5^6(x-5)^4· x\,dx integralni hisoblang.

$\int\limits_5^6\left(x-5\right)^4\cdot x\,dx$ integralni shakl almashtirish orqali hisoblaymiz. $\int\limits_5^6\left(x-5\right)^4\cdot x\,dx=\int\limits_5^6\left(x-5\right)^4\cdot\left(\left(x-5\right)+5\right)dx=\int\limits_5^6\left(\left(x-5\right)^5+5\left(x-5\right)^4\right)dx=\left.\left(\frac{\left(x-5\right)^6}{6}+\left(x-5\right)^5\right)\right|_5^6=\frac{1}{6}+1-0=1\frac{1}{6}.$

Manba: UZBMB namunaviy test topshiriqlari va ularni yechish bo‘yicha tavsiyalar (2020). M.A.Mirzaahmedov va boshqalar. Matematika, umumiy o‘rta ta’lim maktablarining 11-sinflari va o‘rta maxsus, kasb-hunar ta’limi muassasalari uchun darslik. “ZAMIN NASHR”, Toshkent – 2018