Whakaoti i te ∫ (from 0 to 10) of x^2+5x+2=

$$\int _ { 0 } ^ { 10 } x ^ { 2 } + 5 x + 2 =$$

Aromātai

$$\frac{1810}{3}\approx 603.333333333$$

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.

$$\frac{10^{3}}{3}+\frac{5}{2}\times 10^{2}+2\times 10-\left(\frac{0^{3}}{3}+\frac{5}{2}\times 0^{2}+2\times 0\right)$$

Whakarūnātia.

$$\frac{1810}{3}$$