∫ (from - 1 to 1) of 2x^2+4 wrt x eching

$$\int _ { - 1 } ^ { 1 } 2 x ^ { 2 } + 4 d x$$

Baholash

$$\frac{28}{3}\approx 9,333333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 4 integralini toping.

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

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

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

Qisqartirish.

$$\frac{28}{3}$$