∫ (from 1 to 2) of (x+x^2+x^4) wrt x eching

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

Baholash

$$\frac{301}{30}\approx 10,033333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

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.

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

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.

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

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{4}\mathrm{d}x integralni \frac{x^{5}}{5} bilan almashtiring.

$$\frac{x^{2}}{2}+\frac{x^{3}}{3}+\frac{x^{5}}{5}$$

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

$$\frac{2^{2}}{2}+\frac{2^{3}}{3}+\frac{2^{5}}{5}-\left(\frac{1^{2}}{2}+\frac{1^{3}}{3}+\frac{1^{5}}{5}\right)$$

Qisqartirish.

$$\frac{301}{30}$$