∫ (from 1 to 2) of 4x^2+x eching

$$\int _ { 1 } ^ { 2 } 4 x ^ { 2 } + x$$

Baholash

$$\frac{65}{6}\approx 10,833333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

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.

$$\frac{4x^{3}}{3}+\frac{x^{2}}{2}$$

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

$$\frac{4}{3}\times 2^{3}+\frac{2^{2}}{2}-\left(\frac{4}{3}\times 1^{3}+\frac{1^{2}}{2}\right)$$

Qisqartirish.

$$\frac{65}{6}$$