Whakaoti i te ∫ (from - 1 to 1) of (1-y)y wrt y

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

Aromātai

$$-\frac{2}{3}\approx -0.666666667$$

Ngā Upane Otinga

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

$$\int _{-1}^{1}y-y^{2}\mathrm{d}y$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

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}.

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

Ko te tau tōpū tautuhi ko te pārōnaki kōaro o te kīanga i aromātaitia i te tepe tōrunga o te pāwhaitua, tangohia te pārōnaki kōaro i aromātaitia i te tepe tōraro o te pāwhaitua.

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

Whakarūnātia.

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