∫ (from -1 to 3) of x^3+1 wrt x eching

$$\int_{ -1 }^{ 3 } { x }^{ 3 } +1 d x$$

Baholash

$$24$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{3}+1\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{3}\mathrm{d}x+\int 1\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring.

$$\frac{x^{4}}{4}+\int 1\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 1 integralini toping.

$$\frac{x^{4}}{4}+x$$

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

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

Qisqartirish.

$$24$$