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

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

Baholash

$$0$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}+2x+1\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int 2x\mathrm{d}x+\int 1\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int x^{2}\mathrm{d}x+2\int x\mathrm{d}x+\int 1\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+2\int x\mathrm{d}x+\int 1\mathrm{d}x$$

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

$$\frac{x^{3}}{3}+x^{2}+\int 1\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 1 integralini toping.

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

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

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

Qisqartirish.

$$0$$