Whakaoti i te ∫ (from 2 to 3) of (x-2)^2 wrt x

$$\int _ { 2 } ^ { 3 } ( x - 2 ) ^ { 2 } d x$$

Aromātai

$$\frac{1}{3}\approx 0.333333333$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$\int _{2}^{3}x^{2}-4x+4\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int x^{2}-4x+4\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int x^{2}\mathrm{d}x+\int -4x\mathrm{d}x+\int 4\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int x^{2}\mathrm{d}x-4\int x\mathrm{d}x+\int 4\mathrm{d}x$$

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

$$\frac{x^{3}}{3}-4\int x\mathrm{d}x+\int 4\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia -4 ki te \frac{x^{2}}{2}.

$$\frac{x^{3}}{3}-2x^{2}+\int 4\mathrm{d}x$$

Kimihia te tau tōpū o 4 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{x^{3}}{3}-2x^{2}+4x$$

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.

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

Whakarūnātia.

$$\frac{1}{3}$$