∫ (from 2 to 10) of (x^3+4x+9) eching

$$\int _ { 2 } ^ { 10 } ( x ^ { 3 } + 4 x + 9 )$$

Baholash

$$2760$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{3}+4x+9\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{3}\mathrm{d}x+\int 4x\mathrm{d}x+\int 9\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int x^{3}\mathrm{d}x+4\int x\mathrm{d}x+\int 9\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring.

$$\frac{x^{4}}{4}+4\int x\mathrm{d}x+\int 9\mathrm{d}x$$

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

$$\frac{x^{4}}{4}+2x^{2}+\int 9\mathrm{d}x$$

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

$$\frac{x^{4}}{4}+2x^{2}+9x$$

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

$$\frac{10^{4}}{4}+2\times 10^{2}+9\times 10-\left(\frac{2^{4}}{4}+2\times 2^{2}+9\times 2\right)$$

Qisqartirish.

$$2760$$