Whakaoti i te ∫ (from 0 to frac { 1) of {2}}(2y-3y^2-y^2) wrt y

$$\int _ { 0 } ^ { \frac { 1 } { 2 } } ( 2 y - 3 y ^ { 2 } - y ^ { 2 } ) d y$$

Aromātai

$$\frac{1}{12}\approx 0.083333333$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 2y-3y^{2}-y^{2}\mathrm{d}y$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 2y\mathrm{d}y+\int -3y^{2}\mathrm{d}y+\int -y^{2}\mathrm{d}y$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$2\int y\mathrm{d}y-3\int y^{2}\mathrm{d}y-\int y^{2}\mathrm{d}y$$

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}. Whakareatia 2 ki te \frac{y^{2}}{2}.

$$y^{2}-3\int y^{2}\mathrm{d}y-\int y^{2}\mathrm{d}y$$

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

$$y^{2}-y^{3}-\int y^{2}\mathrm{d}y$$

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}.

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

Whakarūnātia.

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

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.

$$\left(\frac{1}{2}\right)^{2}-\frac{4}{3}\times \left(\frac{1}{2}\right)^{3}-\left(0^{2}-\frac{4}{3}\times 0^{3}\right)$$

Whakarūnātia.

$$\frac{1}{12}$$