∫ (from 0 to 8) of V(t)dt eching

$$\int _ { 0 } ^ { 8 } V ( t ) d t$$

Baholash

$$32V$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

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

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

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.

$$V\times \frac{t^{2}}{2}$$

Qisqartirish.

$$\frac{Vt^{2}}{2}$$

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

$$\frac{1}{2}V\times 8^{2}-\frac{1}{2}V\times 0^{2}$$

Qisqartirish.

$$32V$$

V ga nisbatan hosilani topish

$$32$$