Whakaoti i te ∫ 4x^3y wrt y

$$\int 4 x ^ { 3 } y d y$$

Aromātai

$$2y^{2}x^{3}+С$$

Ngā Upane Otinga

Whakatauwehetia te pūmau mā te whakamahi i te \int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y.

$$4x^{3}\int y\mathrm{d}y$$

Nā te mea \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int y\mathrm{d}y ki te \frac{y^{2}}{2}.

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

Whakarūnātia.

$$2x^{3}y^{2}$$

Mēnā ko F\left(y\right) he pārōnaki kōaro o f\left(y\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(y\right) ka whakaaturia e F\left(y\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.

$$2x^{3}y^{2}+С$$

Kimi Pārōnaki e ai ki x

$$6\left(xy\right)^{2}$$