∫ (from 2 to 8) of (3x-9) wrt x eching

$$\int _ { 2 } ^ { 8 } ( 3 x - 9 ) d x$$

Baholash

$$36$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 3x-9\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 3x\mathrm{d}x+\int -9\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$3\int x\mathrm{d}x+\int -9\mathrm{d}x$$

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

$$\frac{3x^{2}}{2}+\int -9\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -9 integralini toping.

$$\frac{3x^{2}}{2}-9x$$

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

$$\frac{3}{2}\times 8^{2}-9\times 8-\left(\frac{3}{2}\times 2^{2}-9\times 2\right)$$

Qisqartirish.

$$36$$