∫ (from 10 to 20) of (x^2-1)e^-02x wrt x eching

$$\int _ { 10 } ^ { 20 } ( x ^ { 2 } - 1 ) e ^ { - 02 x } d x$$

Baholash

$$\frac{6970}{3}\approx 2323,333333333$$

Yechim qadamlari

0 hosil qilish uchun 0 va 2 ni ko'paytirish.

$$\int _{10}^{20}\left(x^{2}-1\right)e^{0x}\mathrm{d}x$$

Har qanday sonni nolga ko‘paytirsangiz, nol chiqadi.

$$\int _{10}^{20}\left(x^{2}-1\right)e^{0}\mathrm{d}x$$

0 daraja ko‘rsatkichini e ga hisoblang va 1 ni qiymatni oling.

$$\int _{10}^{20}\left(x^{2}-1\right)\times 1\mathrm{d}x$$

x^{2}-1 ga 1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\int _{10}^{20}x^{2}-1\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int x^{2}-1\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int -1\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring.

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

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

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

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

$$\frac{20^{3}}{3}-20-\left(\frac{10^{3}}{3}-10\right)$$

Qisqartirish.

$$\frac{6970}{3}$$