∫ (from 2 to 4) of (3x^2-8x+2) wrt x eching

$$\int _ { 2 } ^ { 4 } ( 3 x ^ { 2 } - 8 x + 2 ) d x$$

Baholash

$$12$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 3x^{2}-8x+2\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 3x^{2}\mathrm{d}x+\int -8x\mathrm{d}x+\int 2\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$3\int x^{2}\mathrm{d}x-8\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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

$$x^{3}-8\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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. -8 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

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

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

$$x^{3}-4x^{2}+2x$$

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

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

Qisqartirish.

$$12$$