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

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

Baholash

$$\frac{4-3\cos(1)}{3}\approx 0,793031027$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}+\sin(x)\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int \sin(x)\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring.

$$\frac{x^{3}}{3}+\int \sin(x)\mathrm{d}x$$

Natijani olish uchun umumiy integrallar jadvalidagi \int \sin(x)\mathrm{d}x=-\cos(x) integralidan foydalaning.

$$\frac{x^{3}}{3}-\cos(x)$$

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

$$\frac{1^{3}}{3}-\cos(1)-\left(\frac{0^{3}}{3}-\cos(0)\right)$$

Qisqartirish.

$$\frac{1}{3}\left(4-3\cos(1)\right)$$