∫ (from 0 to 8) of x^2+sinx wrt x eching

$$\int _ { 0 } ^ { 8 } x ^ { 2 } + \sin x d x$$

Baholash

$$\frac{515-3\cos(8)}{3}\approx 171,8121667$$

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.

$$\frac{8^{3}}{3}-\cos(8)-\left(\frac{0^{3}}{3}-\cos(0)\right)$$

Qisqartirish.

$$\frac{1}{3}\left(-3\cos(8)+515\right)$$