Whakaoti i te ∫ (from 0 to 1) of 1/3-1/3y^3 wrt y

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

Aromātai

$$\frac{1}{4}=0.25$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{1-y^{3}}{3}\mathrm{d}y$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{1}{3}\mathrm{d}y+\int -\frac{y^{3}}{3}\mathrm{d}y$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int \frac{1}{3}\mathrm{d}y-\frac{\int y^{3}\mathrm{d}y}{3}$$

Kimihia te tau tōpū o \frac{1}{3} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}y=ay.

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

Nā te mea \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int y^{3}\mathrm{d}y ki te \frac{y^{4}}{4}. Whakareatia -\frac{1}{3} ki te \frac{y^{4}}{4}.

$$\frac{y}{3}-\frac{y^{4}}{12}$$

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.

$$\frac{1}{3}\times 1-\frac{1^{4}}{12}-\left(\frac{1}{3}\times 0-\frac{0^{4}}{12}\right)$$

Whakarūnātia.

$$\frac{1}{4}$$