Whakaoti i te ∫ (from 300 to 400) of (26+33*10^-2*x-3*1*10^-5*x^2) wrt x

$$\int _ { 300 } ^ { 400 } ( 26 + 33 \times 10 ^ { - 2 } \cdot x - 3 \cdot 1 \times 10 ^ { - 5 } \cdot x ^ { 2 } ) d x$$

Aromātai

$$13780$$

Ngā Upane Otinga

Tātaihia te 10 mā te pū o -2, kia riro ko \frac{1}{100}.

$$\int _{300}^{400}26+33\times \frac{1}{100}x-3\times 1\times 10^{-5}x^{2}\mathrm{d}x$$

Whakareatia te 33 ki te \frac{1}{100}, ka \frac{33}{100}.

$$\int _{300}^{400}26+\frac{33}{100}x-3\times 1\times 10^{-5}x^{2}\mathrm{d}x$$

Whakareatia te 3 ki te 1, ka 3.

$$\int _{300}^{400}26+\frac{33}{100}x-3\times 10^{-5}x^{2}\mathrm{d}x$$

Tātaihia te 10 mā te pū o -5, kia riro ko \frac{1}{100000}.

$$\int _{300}^{400}26+\frac{33}{100}x-3\times \frac{1}{100000}x^{2}\mathrm{d}x$$

Whakareatia te 3 ki te \frac{1}{100000}, ka \frac{3}{100000}.

$$\int _{300}^{400}26+\frac{33}{100}x-\frac{3}{100000}x^{2}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 26+\frac{33x}{100}-\frac{3x^{2}}{100000}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 26\mathrm{d}x+\int \frac{33x}{100}\mathrm{d}x+\int -\frac{3x^{2}}{100000}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 26\mathrm{d}x+\frac{33\int x\mathrm{d}x}{100}-\frac{3\int x^{2}\mathrm{d}x}{100000}$$

Kimihia te tau tōpū o 26 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$26x+\frac{33\int x\mathrm{d}x}{100}-\frac{3\int x^{2}\mathrm{d}x}{100000}$$

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 \frac{33}{100} ki te \frac{x^{2}}{2}.

$$26x+\frac{33x^{2}}{200}-\frac{3\int x^{2}\mathrm{d}x}{100000}$$

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 -\frac{3}{100000} ki te \frac{x^{3}}{3}.

$$26x+\frac{33x^{2}}{200}-\frac{x^{3}}{100000}$$

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.

$$26\times 400+\frac{33}{200}\times 400^{2}-\frac{400^{3}}{100000}-\left(26\times 300+\frac{33}{200}\times 300^{2}-\frac{300^{3}}{100000}\right)$$

Whakarūnātia.

$$13780$$