∫ (from 0 to 17) of (9x^2+48x^3) eching

$$\int _ { 0 } ^ { 17 } ( 9 x ^ { 2 } + 48 x ^ { 3 } )$$

Baholash

$$1016991$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 9x^{2}+48x^{3}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 9x^{2}\mathrm{d}x+\int 48x^{3}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$9\int x^{2}\mathrm{d}x+48\int x^{3}\mathrm{d}x$$

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

$$3x^{3}+48\int x^{3}\mathrm{d}x$$

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

$$3x^{3}+12x^{4}$$

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

$$3\times 17^{3}+12\times 17^{4}-\left(3\times 0^{3}+12\times 0^{4}\right)$$

Qisqartirish.

$$1016991$$