∫ (from - 1 to 1) of (x+k) eching

$$\int _ { - 1 } ^ { 1 } ( x + k )$$

Baholash

$$2k$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x+k\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x\mathrm{d}x+\int k\mathrm{d}x$$

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.

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

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

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

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

$$\frac{1^{2}}{2}+k\times 1-\left(\frac{\left(-1\right)^{2}}{2}+k\left(-1\right)\right)$$

Qisqartirish.

$$2k$$

k ga nisbatan hosilani topish

$$2$$