∫ (from 0 to 5) of 2left(1-xright) wrt x eching

$$\int_{ 0 }^{ 5 } 2 \left( 1-x \right) d x$$

Baholash

$$-15$$

Yechim qadamlari

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

$$\int _{0}^{5}2-2x\mathrm{d}x$$

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 2 integralini toping.

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

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. -2 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$2x-x^{2}$$

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

$$2\times 5-5^{2}-\left(2\times 0-0^{2}\right)$$

Qisqartirish.

$$-15$$