f ( x ) = ∫ (from 3 to x) of t^3dt eching

$$f ( x ) = \int _ { 3 } ^ { x } t ^ { 3 } d t$$

Baholash

$$\frac{x^{4}-81}{4}$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int t^{3}\mathrm{d}t$$

k\neq -1 uchun integral \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} boʻlgani uchun, \int t^{3}\mathrm{d}t integralni \frac{t^{4}}{4} bilan almashtiring.

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

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

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

Qisqartirish.

$$\frac{-81+x^{4}}{4}$$

x ga nisbatan hosilani topish

$$x^{3}$$