∫ (from 0 to 8) of (-133x)(-1/12x) wrt x eching

$$\int_{ 0 }^{ 8 } (-133x)(- \frac{ 1 }{ 12 } x) d x$$

Baholash

$$\frac{17024}{9}\approx 1891,555555556$$

Yechim qadamlari

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

$$\int _{0}^{8}-133x^{2}\left(-\frac{1}{12}\right)\mathrm{d}x$$

-133\left(-\frac{1}{12}\right) ni yagona kasrga aylantiring.

$$\int _{0}^{8}\frac{-133\left(-1\right)}{12}x^{2}\mathrm{d}x$$

133 hosil qilish uchun -133 va -1 ni ko'paytirish.

$$\int _{0}^{8}\frac{133}{12}x^{2}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int \frac{133x^{2}}{12}\mathrm{d}x$$

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

$$\frac{133\int x^{2}\mathrm{d}x}{12}$$

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.

$$\frac{133x^{3}}{36}$$

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

$$\frac{133}{36}\times 8^{3}-\frac{133}{36}\times 0^{3}$$

Qisqartirish.

$$\frac{17024}{9}$$