Whakaoti i te ∫ (from - 2 to 1) of (x^3-3x+2)

$$\int _ { - 2 } ^ { 1 } ( x ^ { 3 } - 3 x + 2 )$$

Aromātai

$$\frac{27}{4}=6.75$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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

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

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 -3 ki te \frac{x^{2}}{2}.

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

Kimihia te tau tōpū o 2 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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

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.

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

Whakarūnātia.

$$\frac{27}{4}$$