∫ (from 05 to 1) of p^7(1-p)dp eching

$$\int _ { 05 } ^ { 1 } p ^ { 7 } ( 1 - p ) d p$$

Baholash

$$\frac{1}{72}\approx 0,013888889$$

Yechim qadamlari

p^{7} ga 1-p ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{0\times 5}^{1}p^{7}-p^{8}\mathrm{d}p$$

0 hosil qilish uchun 0 va 5 ni ko'paytirish.

$$\int _{0}^{1}p^{7}-p^{8}\mathrm{d}p$$

Avval noaniq integralni baholang.

$$\int p^{7}-p^{8}\mathrm{d}p$$

Summani muddatma-muddat integratsiya qiling.

$$\int p^{7}\mathrm{d}p+\int -p^{8}\mathrm{d}p$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int p^{7}\mathrm{d}p-\int p^{8}\mathrm{d}p$$

k\neq -1 uchun integral \int p^{k}\mathrm{d}p=\frac{p^{k+1}}{k+1} boʻlgani uchun, \int p^{7}\mathrm{d}p integralni \frac{p^{8}}{8} bilan almashtiring.

$$\frac{p^{8}}{8}-\int p^{8}\mathrm{d}p$$

k\neq -1 uchun integral \int p^{k}\mathrm{d}p=\frac{p^{k+1}}{k+1} boʻlgani uchun, \int p^{8}\mathrm{d}p integralni \frac{p^{9}}{9} bilan almashtiring. -1 ni \frac{p^{9}}{9} marotabaga ko'paytirish.

$$\frac{p^{8}}{8}-\frac{p^{9}}{9}$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$\frac{1^{8}}{8}-\frac{1^{9}}{9}-\left(\frac{0^{8}}{8}-\frac{0^{9}}{9}\right)$$

Qisqartirish.

$$\frac{1}{72}$$