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

$$\int _ { 0 } ^ { 3 } x ^ { 3 } - 2 x ^ { 2 } d x$$

Baholash

$$\frac{9}{4}=2,25$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring.

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

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.

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

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

$$\frac{3^{4}}{4}-\frac{2}{3}\times 3^{3}-\left(\frac{0^{4}}{4}-\frac{2}{3}\times 0^{3}\right)$$

Qisqartirish.

$$\frac{9}{4}$$