∫ (from - 1 to 1) of (3-y) wrt y eching

$$\int _ { - 1 } ^ { 1 } ( 3 - y ) d y$$

Baholash

$$6$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 3-y\mathrm{d}y$$

Summani muddatma-muddat integratsiya qiling.

$$\int 3\mathrm{d}y+\int -y\mathrm{d}y$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 3\mathrm{d}y-\int y\mathrm{d}y$$

\int a\mathrm{d}y=ay umumiy integrallar qoidasi jadvalidan foydalanib, 3 integralini toping.

$$3y-\int y\mathrm{d}y$$

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.

$$3y-\frac{y^{2}}{2}$$

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

$$3\times 1-\frac{1^{2}}{2}-\left(3\left(-1\right)-\frac{\left(-1\right)^{2}}{2}\right)$$

Qisqartirish.

$$6$$