∫ (from 0 to 1) of (x^2+e^2) wrt x eching

$$\int _ { 0 } ^ { 1 } ( x ^ { 2 } + e ^ { 2 } ) d x$$

Baholash

$$e^{2}+\frac{1}{3}\approx 7,722389432$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}+e^{2}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int e^{2}\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+\int e^{2}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, e^{2} integralini toping.

$$\frac{x^{3}}{3}+e^{2}x$$

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

$$\frac{1^{3}}{3}+e^{2}\times 1-\left(\frac{0^{3}}{3}+e^{2}\times 0\right)$$

Qisqartirish.

$$\frac{1}{3}+e^{2}$$