∫ (from 0 to 3) of (91x+198)(-6-x) wrt x eching

$$\int_{ 0 }^{ 3 } (91x+198)(-6-x) d x$$

Baholash

$$-7731$$

Yechim qadamlari

91x+198 ifodaning har bir elementini -6-x ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\int _{0}^{3}-546x-91x^{2}-1188-198x\mathrm{d}x$$

-744x ni olish uchun -546x va -198x ni birlashtirish.

$$\int _{0}^{3}-744x-91x^{2}-1188\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int -744x-91x^{2}-1188\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int -744x\mathrm{d}x+\int -91x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-744\int x\mathrm{d}x-91\int x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. -744 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$-372x^{2}-91\int x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring. -91 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$-372x^{2}-\frac{91x^{3}}{3}+\int -1188\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -1188 integralini toping.

$$-372x^{2}-\frac{91x^{3}}{3}-1188x$$

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

$$-372\times 3^{2}-\frac{91}{3}\times 3^{3}-1188\times 3-\left(-372\times 0^{2}-\frac{91}{3}\times 0^{3}-1188\times 0\right)$$

Qisqartirish.

$$-7731$$