Whakaoti i te ∫ (from 3 to 4) of (x^2+5x+2) wrt x

$$\int _ { 3 } ^ { 4 } ( x ^ { 2 } + 5 x + 2 ) d x$$

Aromātai

$$\frac{191}{6}\approx 31.833333333$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int x^{2}+5x+2\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int x^{2}\mathrm{d}x+\int 5x\mathrm{d}x+\int 2\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int x^{2}\mathrm{d}x+5\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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

$$\frac{x^{3}}{3}+5\int x\mathrm{d}x+\int 2\mathrm{d}x$$

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

$$\frac{x^{3}}{3}+\frac{5x^{2}}{2}+\int 2\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+\frac{5x^{2}}{2}+2x$$

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.

$$\frac{4^{3}}{3}+\frac{5}{2}\times 4^{2}+2\times 4-\left(\frac{3^{3}}{3}+\frac{5}{2}\times 3^{2}+2\times 3\right)$$

Whakarūnātia.

$$\frac{191}{6}$$