∫ (from - 1 to 1) of x-x^3 wrt x eching

$$\int _ { - 1 } ^ { 1 } x - x ^ { 3 } d x$$

Baholash

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Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

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. -1 ni \frac{x^{4}}{4} marotabaga ko'paytirish.

$$\frac{x^{2}}{2}-\frac{x^{4}}{4}$$

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

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

Qisqartirish.

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