∫ (from 1 to 5) of 4x^2 eching

$$\int _ { 1 } ^ { 5 } 4 x ^ { 2 }$$

Baholash

$$\frac{496}{3}\approx 165,333333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 4x^{2}\mathrm{d}x$$

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

$$4\int x^{2}\mathrm{d}x$$

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.

$$\frac{4x^{3}}{3}$$

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

$$\frac{4}{3}\times 5^{3}-\frac{4}{3}\times 1^{3}$$

Qisqartirish.

$$\frac{496}{3}$$