∫ (from 0 to 2) of x(x-2) wrt x eching

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

Baholash

$$-\frac{4}{3}\approx -1,333333333$$

Yechim qadamlari

x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{0}^{2}x^{2}-2x\mathrm{d}x$$

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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.

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

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.

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

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

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

Qisqartirish.

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