∫ (from - 3 to 3) of (x^2+x) wrt x eching

$$\int _ { - 3 } ^ { 3 } ( x ^ { 2 } + x ) d x$$

Baholash

$$18$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

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.

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

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

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

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

$$\frac{3^{3}}{3}+\frac{3^{2}}{2}-\left(\frac{\left(-3\right)^{3}}{3}+\frac{\left(-3\right)^{2}}{2}\right)$$

Qisqartirish.

$$18$$