∫ (from 2 to 4) of 3x^5-2x^3+x eching

$$\int _ { 2 } ^ { 4 } 3 x ^ { 5 } - 2 x ^ { 3 } + x$$

Baholash

$$1902$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 3x^{5}-2x^{3}+x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 3x^{5}\mathrm{d}x+\int -2x^{3}\mathrm{d}x+\int x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$3\int x^{5}\mathrm{d}x-2\int x^{3}\mathrm{d}x+\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{5}\mathrm{d}x integralni \frac{x^{6}}{6} bilan almashtiring. 3 ni \frac{x^{6}}{6} marotabaga ko'paytirish.

$$\frac{x^{6}}{2}-2\int x^{3}\mathrm{d}x+\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring. -2 ni \frac{x^{4}}{4} marotabaga ko'paytirish.

$$\frac{x^{6}}{2}-\frac{x^{4}}{2}+\int x\mathrm{d}x$$

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.

$$\frac{x^{6}-x^{4}+x^{2}}{2}$$

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

$$\frac{4^{6}}{2}-\frac{4^{4}}{2}+\frac{4^{2}}{2}-\left(\frac{2^{6}}{2}-\frac{2^{4}}{2}+\frac{2^{2}}{2}\right)$$

Qisqartirish.

$$1902$$