∫ (from 0 to 1) of (x^18+18^x) wrt x eching

$$\int _ { 0 } ^ { 1 } ( x ^ { 18 } + 18 ^ { x } ) d x$$

Baholash

$$\frac{17}{\ln(18)}+\frac{1}{19}\approx 5,934227935$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{18}+18^{x}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{18}\mathrm{d}x+\int 18^{x}\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{18}\mathrm{d}x integralni \frac{x^{19}}{19} bilan almashtiring.

$$\frac{x^{19}}{19}+\int 18^{x}\mathrm{d}x$$

Natijani olish uchun umumiy integrallar jadvalidagi \int x^{k}\mathrm{d}k=\frac{x^{k}}{\ln(x)} integralidan foydalaning.

$$\frac{x^{19}}{19}+\frac{18^{x}}{\ln(18)}$$

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

$$\frac{1^{19}}{19}+18^{1}\ln(18)^{-1}-\left(\frac{0^{19}}{19}+18^{0}\ln(18)^{-1}\right)$$

Qisqartirish.

$$\frac{1}{19}+\frac{17}{\ln(18)}$$