∫ (from 2 to 4) of 4-y wrt y eching

$$\int_{ 2 }^{ 4 } 4-y d y$$

Baholash

$$2$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 4-y\mathrm{d}y$$

Summani muddatma-muddat integratsiya qiling.

$$\int 4\mathrm{d}y+\int -y\mathrm{d}y$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 4\mathrm{d}y-\int y\mathrm{d}y$$

\int a\mathrm{d}y=ay umumiy integrallar qoidasi jadvalidan foydalanib, 4 integralini toping.

$$4y-\int y\mathrm{d}y$$

k\neq -1 uchun integral \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} boʻlgani uchun, \int y\mathrm{d}y integralni \frac{y^{2}}{2} bilan almashtiring. -1 ni \frac{y^{2}}{2} marotabaga ko'paytirish.

$$4y-\frac{y^{2}}{2}$$

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

$$4\times 4-\frac{4^{2}}{2}-\left(4\times 2-\frac{2^{2}}{2}\right)$$

Qisqartirish.

$$2$$