∫ (from 02 to 12) of (-800V+1160)dV eching

$$\int _ { 02 } ^ { 12 } ( - 800 V + 1160 ) d V$$

Baholash

$$-43680$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int -800V+1160\mathrm{d}V$$

Summani muddatma-muddat integratsiya qiling.

$$\int -800V\mathrm{d}V+\int 1160\mathrm{d}V$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-800\int V\mathrm{d}V+\int 1160\mathrm{d}V$$

k\neq -1 uchun integral \int V^{k}\mathrm{d}V=\frac{V^{k+1}}{k+1} boʻlgani uchun, \int V\mathrm{d}V integralni \frac{V^{2}}{2} bilan almashtiring. -800 ni \frac{V^{2}}{2} marotabaga ko'paytirish.

$$-400V^{2}+\int 1160\mathrm{d}V$$

\int a\mathrm{d}V=aV umumiy integrallar qoidasi jadvalidan foydalanib, 1160 integralini toping.

$$-400V^{2}+1160V$$

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

$$-400\times 12^{2}+1160\times 12-\left(-400\times \left(0\times 2\right)^{2}+1160\times 0\times 2\right)$$

Qisqartirish.

$$-43680$$