∫ (from - 4 to 4) of x^2-4 wrt x eching

$$\int _ { - 4 } ^ { 4 } x ^ { 2 } - 4 d x$$

Baholash

$$\frac{32}{3}\approx 10,666666667$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}-4\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int -4\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+\int -4\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -4 integralini toping.

$$\frac{x^{3}}{3}-4x$$

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

$$\frac{4^{3}}{3}-4\times 4-\left(\frac{\left(-4\right)^{3}}{3}-4\left(-4\right)\right)$$

Qisqartirish.

$$\frac{32}{3}$$