∫ (from 0 to 10) of x^2+5x+2= eching

$$\int _ { 0 } ^ { 10 } x ^ { 2 } + 5 x + 2 =$$

Baholash

$$\frac{1810}{3}\approx 603,333333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

$$\frac{x^{3}}{3}+5\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+\frac{5x^{2}}{2}+\int 2\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 2 integralini toping.

$$\frac{x^{3}}{3}+\frac{5x^{2}}{2}+2x$$

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

$$\frac{10^{3}}{3}+\frac{5}{2}\times 10^{2}+2\times 10-\left(\frac{0^{3}}{3}+\frac{5}{2}\times 0^{2}+2\times 0\right)$$

Qisqartirish.

$$\frac{1810}{3}$$