∫ (from 1 to 2) of (15x^2-12x) wrt x eching

$$\int_{ 1 }^{ 2 } (15 { x }^{ 2 } -12x) d x$$

Baholash

$$17$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 15x^{2}-12x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 15x^{2}\mathrm{d}x+\int -12x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$15\int x^{2}\mathrm{d}x-12\int x\mathrm{d}x$$

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. 15 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$5x^{3}-12\int x\mathrm{d}x$$

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. -12 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$5x^{3}-6x^{2}$$

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

$$5\times 2^{3}-6\times 2^{2}-\left(5\times 1^{3}-6\times 1^{2}\right)$$

Qisqartirish.

$$17$$