∫ 6y^3 wrt y eching

$$\int{ 6 { y }^{ 3 } }d y$$

Baholash

$$\frac{3y^{4}}{2}+С$$

Yechim qadamlari

\int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y yordamidan konstantani qavsdan tashqariga chiqaring.

$$6\int y^{3}\mathrm{d}y$$

k\neq -1 uchun integral \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} boʻlgani uchun, \int y^{3}\mathrm{d}y integralni \frac{y^{4}}{4} bilan almashtiring. 6 ni \frac{y^{4}}{4} marotabaga ko'paytirish.

$$\frac{3y^{4}}{2}$$

Агар F\left(y\right)f\left(y\right) ning dastlabki holati boʻlsa, u holatda f\left(y\right) ning barcha dastlabki holatlari toʻplami F\left(y\right)+C tarafidan belgilanadi. Shu sababli natijaga C\in \mathrm{R} integrallash konstantasini qoʻshing.

$$\frac{3y^{4}}{2}+С$$

y ga nisbatan hosilani topish

$$6y^{3}$$