F ( x ) = ∫ (from 1 to x) of (t^2-4)dt eching

$$F ( x ) = \int _ { 1 } ^ { x } ( t ^ { 2 } - 4 ) d t$$

Baholash

$$\frac{x^{3}-12x+11}{3}$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int t^{2}-4\mathrm{d}t$$

Summani muddatma-muddat integratsiya qiling.

$$\int t^{2}\mathrm{d}t+\int -4\mathrm{d}t$$

k\neq -1 uchun integral \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} boʻlgani uchun, \int t^{2}\mathrm{d}t integralni \frac{t^{3}}{3} bilan almashtiring.

$$\frac{t^{3}}{3}+\int -4\mathrm{d}t$$

\int a\mathrm{d}t=at umumiy integrallar qoidasi jadvalidan foydalanib, -4 integralini toping.

$$\frac{t^{3}}{3}-4t$$

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

$$\frac{x^{3}}{3}-4x-\left(\frac{1^{3}}{3}-4\right)$$

Qisqartirish.

$$\frac{x^{3}}{3}-4x+\frac{11}{3}$$

x ga nisbatan hosilani topish

$$x^{2}-4$$