∫ xydeltaxdeltay eching

$$\int x y \delta x \delta y$$

Baholash

$$\frac{x^{3}\left(y\delta \right)^{2}}{3}+С$$

Yechim qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\int x^{2}y\delta \delta y\mathrm{d}x$$

y^{2} hosil qilish uchun y va y ni ko'paytirish.

$$\int x^{2}y^{2}\delta \delta \mathrm{d}x$$

\delta ^{2} hosil qilish uchun \delta va \delta ni ko'paytirish.

$$\int x^{2}y^{2}\delta ^{2}\mathrm{d}x$$

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

$$y^{2}\delta ^{2}\int x^{2}\mathrm{d}x$$

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.

$$y^{2}\delta ^{2}\times \frac{x^{3}}{3}$$

Qisqartirish.

$$\frac{y^{2}\delta ^{2}x^{3}}{3}$$

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

$$\frac{y^{2}\delta ^{2}x^{3}}{3}+С$$

x ga nisbatan hosilani topish

$$\left(xy\delta \right)^{2}$$