Whakaoti i te ∫ y(1-y) wrt y

$$\int y ( 1 - y ) d y$$

Aromātai

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

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te y ki te 1-y.

$$\int y-y^{2}\mathrm{d}y$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int y\mathrm{d}y+\int -y^{2}\mathrm{d}y$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int y\mathrm{d}y-\int y^{2}\mathrm{d}y$$

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}.

$$\frac{y^{2}}{2}-\int y^{2}\mathrm{d}y$$

Nā te mea \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int y^{2}\mathrm{d}y ki te \frac{y^{3}}{3}. Whakareatia -1 ki te \frac{y^{3}}{3}.

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

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.

$$\frac{y^{2}}{2}-\frac{y^{3}}{3}+С$$

Kimi Pārōnaki e ai ki y

$$y\left(1-y\right)$$