∫ (from 5 to 8) of (13-2x) wrt x eching

$$\int _ { 5 } ^ { 8 } ( 13 - 2 x ) d x$$

Baholash

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Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 13-2x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 13\mathrm{d}x+\int -2x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 13\mathrm{d}x-2\int x\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 13 integralini toping.

$$13x-2\int x\mathrm{d}x$$

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. -2 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$13x-x^{2}$$

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

$$13\times 8-8^{2}-\left(13\times 5-5^{2}\right)$$

Qisqartirish.

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