∫ (from 0 to 2) of 5438x7/25x wrt x eching

$$\int_{ 0 }^{ 2 } 5438x \frac{ 7 }{ 25 } x d x$$

Baholash

$$\frac{304528}{75}\approx 4060,373333333$$

Yechim qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\int _{0}^{2}5438x^{2}\times \frac{7}{25}\mathrm{d}x$$

5438\times \frac{7}{25} ni yagona kasrga aylantiring.

$$\int _{0}^{2}\frac{5438\times 7}{25}x^{2}\mathrm{d}x$$

38066 hosil qilish uchun 5438 va 7 ni ko'paytirish.

$$\int _{0}^{2}\frac{38066}{25}x^{2}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int \frac{38066x^{2}}{25}\mathrm{d}x$$

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

$$\frac{38066\int x^{2}\mathrm{d}x}{25}$$

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.

$$\frac{38066x^{3}}{75}$$

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

$$\frac{38066}{75}\times 2^{3}-\frac{38066}{75}\times 0^{3}$$

Qisqartirish.

$$\frac{304528}{75}$$