∫ (from 0 to 12) of (-13/90x^2+13/13x+72/5) wrt x eching

$$\int _ { 0 } ^ { 12 } ( - \frac { 13 } { 90 } x ^ { 2 } + \frac { 13 } { 13 } x + \frac { 72 } { 5 } ) d x$$

Baholash

$$\frac{808}{5}=161,6$$

Yechim qadamlari

1 ni olish uchun 13 ni 13 ga bo‘ling.

$$\int _{0}^{12}-\frac{13}{90}x^{2}+1x+\frac{72}{5}\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int -\frac{13x^{2}}{90}+x+\frac{72}{5}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int -\frac{13x^{2}}{90}\mathrm{d}x+\int x\mathrm{d}x+\int \frac{72}{5}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-\frac{13\int x^{2}\mathrm{d}x}{90}+\int x\mathrm{d}x+\int \frac{72}{5}\mathrm{d}x$$

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. -\frac{13}{90} ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$-\frac{13x^{3}}{270}+\int x\mathrm{d}x+\int \frac{72}{5}\mathrm{d}x$$

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.

$$-\frac{13x^{3}}{270}+\frac{x^{2}}{2}+\int \frac{72}{5}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \frac{72}{5} integralini toping.

$$-\frac{13x^{3}}{270}+\frac{x^{2}}{2}+\frac{72x}{5}$$

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

$$-\frac{13}{270}\times 12^{3}+\frac{12^{2}}{2}+\frac{72}{5}\times 12-\left(-\frac{13}{270}\times 0^{3}+\frac{0^{2}}{2}+\frac{72}{5}\times 0\right)$$

Qisqartirish.

$$\frac{808}{5}$$