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

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

Baholash

$$\frac{129}{2}=64,5$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

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

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 2 integralini toping.

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

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

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

Qisqartirish.

$$\frac{129}{2}$$