∫ (from - 2 to 1) of (x^3-3x+2) eching

$$\int _ { - 2 } ^ { 1 } ( x ^ { 3 } - 3 x + 2 )$$

Baholash

$$\frac{27}{4}=6,75$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

$$\frac{x^{4}}{4}-3\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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. -3 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$\frac{x^{4}}{4}-\frac{3x^{2}}{2}+\int 2\mathrm{d}x$$

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

$$\frac{x^{4}}{4}-\frac{3x^{2}}{2}+2x$$

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

$$\frac{1^{4}}{4}-\frac{3}{2}\times 1^{2}+2\times 1-\left(\frac{\left(-2\right)^{4}}{4}-\frac{3}{2}\left(-2\right)^{2}+2\left(-2\right)\right)$$

Qisqartirish.

$$\frac{27}{4}$$