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

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

Aromātai

$$\frac{7}{3}\approx 2.333333333$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x-1 ki ia tau o x+3.

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

Pahekotia te 3x me -x, ka 2x.

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

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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}.

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

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

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

Kimihia te tau tōpū o -3 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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

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.

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

Whakarūnātia.

$$\frac{7}{3}$$