∫ (from 0 to 1) of x+y wrt x eching

$$\int _ { 0 } ^ { 1 } x + y d x$$

Baholash

$$y = \frac{1}{2} = 0,5$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x+y\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x\mathrm{d}x+\int y\mathrm{d}x$$

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.

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

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

$$\frac{x^{2}}{2}+yx$$

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

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

Qisqartirish.

$$\frac{1}{2}+y$$

y ga nisbatan hosilani topish

$$1$$