∫ (from x = 0 to 20) of x^2 eching

$$\int _ { x = 0 } ^ { 20 } x ^ { 2 }$$

Baholash

$$\frac{8000}{3}\approx 2666,666666667$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

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.

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

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

$$\frac{20^{3}}{3}-\frac{0^{3}}{3}$$

Qisqartirish.

$$\frac{8000}{3}$$