∫ (from 1 to x) of 3tdt eching

$$\int _ { 1 } ^ { x } 3 t d t$$

Baholash

$$\frac{3\left(x^{2}-1\right)}{2}$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

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

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

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

$$\frac{3t^{2}}{2}$$

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

$$\frac{3}{2}x^{2}-\frac{3}{2}\times 1^{2}$$

Qisqartirish.

$$\frac{3x^{2}-3}{2}$$

x ga nisbatan hosilani topish

$$3x$$