∫ (from 2 to 5) of x^2+5 eching

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

Baholash

$$54$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

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.

$$\frac{x^{3}}{3}+\int 5\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 5 integralini toping.

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

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

$$\frac{5^{3}}{3}+5\times 5-\left(\frac{2^{3}}{3}+5\times 2\right)$$

Qisqartirish.

$$54$$