∫ (from 3 to 7) of (5x-20) wrt x eching

$$\int _ { 3 } ^ { 7 } ( 5 x - 20 ) d x$$

Baholash

$$20$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 5x-20\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 5x\mathrm{d}x+\int -20\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$5\int x\mathrm{d}x+\int -20\mathrm{d}x$$

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

$$\frac{5x^{2}}{2}+\int -20\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -20 integralini toping.

$$\frac{5x^{2}}{2}-20x$$

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

$$\frac{5}{2}\times 7^{2}-20\times 7-\left(\frac{5}{2}\times 3^{2}-20\times 3\right)$$

Qisqartirish.

$$20$$