∫ (from 1 to 2) of 5x^2 eching

$$\int _ { 1 } ^ { 2 } 5 x ^ { 2 }$$

Baholash

$$\frac{35}{3}\approx 11,666666667$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

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

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

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.

$$\frac{5x^{3}}{3}$$

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

$$\frac{5}{3}\times 2^{3}-\frac{5}{3}\times 1^{3}$$

Qisqartirish.

$$\frac{35}{3}$$