∫ (from - 1 to 1) of (2x^2*x^3) wrt x eching

$$\int _ { - 1 } ^ { 1 } ( 2 x ^ { 2 } \cdot x ^ { 3 } ) d x$$

Baholash

$$0$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 3 ni qo‘shib, 5 ni oling.

$$\int _{-1}^{1}2x^{5}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int 2x^{5}\mathrm{d}x$$

\int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x yordamidan konstantani qavsdan tashqariga chiqaring.

$$2\int x^{5}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{5}\mathrm{d}x integralni \frac{x^{6}}{6} bilan almashtiring. 2 ni \frac{x^{6}}{6} marotabaga ko'paytirish.

$$\frac{x^{6}}{3}$$

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

$$\frac{1^{6}}{3}-\frac{\left(-1\right)^{6}}{3}$$

Qisqartirish.

$$0$$