Whakaoti i te ∫ (from - 4 to 3) of (12-x-x^2) wrt x

$$\int _ { - 4 } ^ { 3 } ( 12 - x - x ^ { 2 } ) d x$$

Aromātai

$$\frac{343}{6}\approx 57.166666667$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 12-x-x^{2}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 12\mathrm{d}x+\int -x\mathrm{d}x+\int -x^{2}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 12\mathrm{d}x-\int x\mathrm{d}x-\int x^{2}\mathrm{d}x$$

Kimihia te tau tōpū o 12 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$12x-\int x\mathrm{d}x-\int x^{2}\mathrm{d}x$$

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 -1 ki te \frac{x^{2}}{2}.

$$12x-\frac{x^{2}}{2}-\int x^{2}\mathrm{d}x$$

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

$$12x-\frac{x^{2}}{2}-\frac{x^{3}}{3}$$

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.

$$12\times 3-\frac{3^{2}}{2}-\frac{3^{3}}{3}-\left(12\left(-4\right)-\frac{\left(-4\right)^{2}}{2}-\frac{\left(-4\right)^{3}}{3}\right)$$

Whakarūnātia.

$$\frac{343}{6}$$