Whakaoti i te ∫ (from 0 to 100) of (x^2+2+3x^4+2e^9) wrt x

$$\int _ { 0 } ^ { 100 } ( x ^ { 2 } + 2 + 3 x ^ { 4 } + 2 e ^ { 9 } ) d x$$

Aromātai

$$200e^{9}+\frac{18001000600}{3}\approx 6001954150.118847847$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int x^{2}+2+3x^{4}+2e^{9}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int x^{2}\mathrm{d}x+\int 2\mathrm{d}x+\int 3x^{4}\mathrm{d}x+\int 2e^{9}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int x^{2}\mathrm{d}x+\int 2\mathrm{d}x+3\int x^{4}\mathrm{d}x+2\int e^{9}\mathrm{d}x$$

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}.

$$\frac{x^{3}}{3}+\int 2\mathrm{d}x+3\int x^{4}\mathrm{d}x+2\int e^{9}\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}+2x+3\int x^{4}\mathrm{d}x+2\int e^{9}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{4}\mathrm{d}x ki te \frac{x^{5}}{5}. Whakareatia 3 ki te \frac{x^{5}}{5}.

$$\frac{x^{3}}{3}+2x+\frac{3x^{5}}{5}+2\int e^{9}\mathrm{d}x$$

Kimihia te tau tōpū o e^{9} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{x^{3}}{3}+2x+\frac{3x^{5}}{5}+2e^{9}x$$

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.

$$\frac{100^{3}}{3}+2\times 100+\frac{3}{5}\times 100^{5}+2e^{9}\times 100-\left(\frac{0^{3}}{3}+2\times 0+\frac{3}{5}\times 0^{5}+2e^{9}\times 0\right)$$

Whakarūnātia.

$$\frac{18001000600}{3}+200e^{9}$$