Whakaoti i te ∫ (from 0 to 3) of (9.1x+19.8)(-6-x) wrt x

$$\int_{ 0 }^{ 3 } (9.1x+19.8)(-6-x) d x$$

Aromātai

$$-773.1$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 9.1x+19.8 ki ia tau o -6-x.

$$\int _{0}^{3}-54.6x-9.1x^{2}-118.8-19.8x\mathrm{d}x$$

Pahekotia te -54.6x me -19.8x, ka -74.4x.

$$\int _{0}^{3}-74.4x-9.1x^{2}-118.8\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -\frac{372x}{5}-\frac{91x^{2}}{10}-118.8\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -\frac{372x}{5}\mathrm{d}x+\int -\frac{91x^{2}}{10}\mathrm{d}x+\int -118.8\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-\frac{372\int x\mathrm{d}x}{5}-\frac{91\int x^{2}\mathrm{d}x}{10}+\int -118.8\mathrm{d}x$$

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 -74.4 ki te \frac{x^{2}}{2}.

$$-\frac{186x^{2}}{5}-\frac{91\int x^{2}\mathrm{d}x}{10}+\int -118.8\mathrm{d}x$$

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 -9.1 ki te \frac{x^{3}}{3}.

$$-\frac{186x^{2}}{5}-\frac{91x^{3}}{30}+\int -118.8\mathrm{d}x$$

Kimihia te tau tōpū o -118.8 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-\frac{186x^{2}}{5}-\frac{91x^{3}}{30}-\frac{594x}{5}$$

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.

$$-\frac{186}{5}\times 3^{2}-\frac{91}{30}\times 3^{3}-118.8\times 3-\left(-\frac{186}{5}\times 0^{2}-\frac{91}{30}\times 0^{3}-118.8\times 0\right)$$

Whakarūnātia.

$$-\frac{7731}{10}$$