∫ (from - 1 to 1) of (4x^2-3) wrt x eching

$$\int _ { - 1 } ^ { 1 } ( 4 x ^ { 2 } - 3 ) d x$$

Baholash

$$-\frac{10}{3}\approx -3,333333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -3 integralini toping.

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

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

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

Qisqartirish.

$$-\frac{10}{3}$$