∫ (from - 2 to 0) of (3x^2+x-1) wrt x eching

$$\int _ { - 2 } ^ { 0 } ( 3 x ^ { 2 } + x - 1 ) d x$$

Baholash

$$4$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

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.

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

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

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

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

$$0^{3}+\frac{0^{2}}{2}-0-\left(\left(-2\right)^{3}+\frac{\left(-2\right)^{2}}{2}-\left(-2\right)\right)$$

Qisqartirish.

$$4$$