∫ (from 1 to 4) of x^2+1/x^3 wrt x eching

$$\int_{ 1 }^{ 4 } { x }^{ 2 } + \frac{ 1 }{ { x }^{ 3 } } d x$$

Baholash

$$\frac{687}{32}=21,46875$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}+\frac{1}{x^{3}}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int \frac{1}{x^{3}}\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+\int \frac{1}{x^{3}}\mathrm{d}x$$

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

$$\frac{x^{3}}{3}-\frac{1}{2x^{2}}$$

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

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

Qisqartirish.

$$\frac{687}{32}$$