Whakaoti i te ∫ (from 2 to 3) of (82^3+3z-1) wrt z=

$$\int _ { 2 } ^ { 3 } ( 82 ^ { 3 } + 3 z - 1 ) d z =$$

Aromātai

$$\frac{1102749}{2}=551374.5$$

Ngā Upane Otinga

Tātaihia te 82 mā te pū o 3, kia riro ko 551368.

$$\int _{2}^{3}551368+3z-1\mathrm{d}z$$

Tangohia te 1 i te 551368, ka 551367.

$$\int _{2}^{3}551367+3z\mathrm{d}z$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 551367+3z\mathrm{d}z$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 551367\mathrm{d}z+\int 3z\mathrm{d}z$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 551367\mathrm{d}z+3\int z\mathrm{d}z$$

Kimihia te tau tōpū o 551367 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}z=az.

$$551367z+3\int z\mathrm{d}z$$

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

$$551367z+\frac{3z^{2}}{2}$$

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.

$$551367\times 3+\frac{3}{2}\times 3^{2}-\left(551367\times 2+\frac{3}{2}\times 2^{2}\right)$$

Whakarūnātia.

$$\frac{1102749}{2}$$