∫ (from 3 to 4) of (x^2+5x+2) wrt x eching

$$\int _ { 3 } ^ { 4 } ( x ^ { 2 } + 5 x + 2 ) d x$$

Baholash

$$\frac{191}{6}\approx 31,833333333$$

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.

$$\frac{4^{3}}{3}+\frac{5}{2}\times 4^{2}+2\times 4-\left(\frac{3^{3}}{3}+\frac{5}{2}\times 3^{2}+2\times 3\right)$$

Qisqartirish.

$$\frac{191}{6}$$