∫ (from 2 to 3) of (82^3+3z-1) wrt z= eching

$$\int _ { 2 } ^ { 3 } ( 82 ^ { 3 } + 3 z - 1 ) d z =$$

Baholash

$$\frac{1102749}{2}=551374,5$$

Yechim qadamlari

3 daraja ko‘rsatkichini 82 ga hisoblang va 551368 ni qiymatni oling.

$$\int _{2}^{3}551368+3z-1\mathrm{d}z$$

551367 olish uchun 551368 dan 1 ni ayirish.

$$\int _{2}^{3}551367+3z\mathrm{d}z$$

Avval noaniq integralni baholang.

$$\int 551367+3z\mathrm{d}z$$

Summani muddatma-muddat integratsiya qiling.

$$\int 551367\mathrm{d}z+\int 3z\mathrm{d}z$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 551367\mathrm{d}z+3\int z\mathrm{d}z$$

\int a\mathrm{d}z=az umumiy integrallar qoidasi jadvalidan foydalanib, 551367 integralini toping.

$$551367z+3\int z\mathrm{d}z$$

k\neq -1 uchun integral \int z^{k}\mathrm{d}z=\frac{z^{k+1}}{k+1} boʻlgani uchun, \int z\mathrm{d}z integralni \frac{z^{2}}{2} bilan almashtiring. 3 ni \frac{z^{2}}{2} marotabaga ko'paytirish.

$$551367z+\frac{3z^{2}}{2}$$

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

$$551367\times 3+\frac{3}{2}\times 3^{2}-\left(551367\times 2+\frac{3}{2}\times 2^{2}\right)$$

Qisqartirish.

$$\frac{1102749}{2}$$