∫ (from 2 to 7) of left(4112x-2left(x-2right)-x-2/2right)7/23 wrt x eching

$$\int_{ 2 }^{ 7 } \left( 4112x-2 \left( x-2 \right) - \frac{ x-2 }{ 2 } \right) \frac{ 7 }{ 23 } d x$$

Baholash

$$\frac{112595}{4}=28148,75$$

Yechim qadamlari

-\frac{5}{2}\left(x-2\right) ni olish uchun -2\left(x-2\right) va -\frac{x-2}{2} ni birlashtirish.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}\left(x-2\right)\right)\times \frac{7}{23}\mathrm{d}x$$

-\frac{5}{2} ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x-\frac{5}{2}\left(-2\right)\right)\times \frac{7}{23}\mathrm{d}x$$

-\frac{5}{2}\left(-2\right) ni yagona kasrga aylantiring.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+\frac{-5\left(-2\right)}{2}\right)\times \frac{7}{23}\mathrm{d}x$$

10 hosil qilish uchun -5 va -2 ni ko'paytirish.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+\frac{10}{2}\right)\times \frac{7}{23}\mathrm{d}x$$

5 ni olish uchun 10 ni 2 ga bo‘ling.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+5\right)\times \frac{7}{23}\mathrm{d}x$$

\frac{8219}{2}x ni olish uchun 4112x va -\frac{5}{2}x ni birlashtirish.

$$\int _{2}^{7}\left(\frac{8219}{2}x+5\right)\times \frac{7}{23}\mathrm{d}x$$

\frac{8219}{2}x+5 ga \frac{7}{23} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{2}^{7}\frac{8219}{2}x\times \frac{7}{23}+5\times \frac{7}{23}\mathrm{d}x$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{8219}{2} ni \frac{7}{23} ga ko‘paytiring.

$$\int _{2}^{7}\frac{8219\times 7}{2\times 23}x+5\times \frac{7}{23}\mathrm{d}x$$

\frac{8219\times 7}{2\times 23} kasridagi ko‘paytirishlarni bajaring.

$$\int _{2}^{7}\frac{57533}{46}x+5\times \frac{7}{23}\mathrm{d}x$$

5\times \frac{7}{23} ni yagona kasrga aylantiring.

$$\int _{2}^{7}\frac{57533}{46}x+\frac{5\times 7}{23}\mathrm{d}x$$

35 hosil qilish uchun 5 va 7 ni ko'paytirish.

$$\int _{2}^{7}\frac{57533}{46}x+\frac{35}{23}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int \frac{57533x}{46}+\frac{35}{23}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int \frac{57533x}{46}\mathrm{d}x+\int \frac{35}{23}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\frac{57533\int x\mathrm{d}x}{46}+\int \frac{35}{23}\mathrm{d}x$$

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. \frac{57533}{46} ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$\frac{57533x^{2}}{92}+\int \frac{35}{23}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \frac{35}{23} integralini toping.

$$\frac{57533x^{2}}{92}+\frac{35x}{23}$$

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

$$\frac{57533}{92}\times 7^{2}+\frac{35}{23}\times 7-\left(\frac{57533}{92}\times 2^{2}+\frac{35}{23}\times 2\right)$$

Qisqartirish.

$$\frac{112595}{4}$$