Whakaoti i te ∫ (from 0 to 4) of (4.4x-4)(-0.2-0.1x) wrt x

$$\int_{ 0 }^{ 4 } (4.4x-4)(-0.2-0.1x) d x$$

Aromātai

$$-\frac{752}{75}\approx -10.026666667$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 4.4x-4 ki ia tau o -0.2-0.1x.

$$\int _{0}^{4}-0.88x-0.44x^{2}+0.8+0.4x\mathrm{d}x$$

Pahekotia te -0.88x me 0.4x, ka -0.48x.

$$\int _{0}^{4}-0.48x-0.44x^{2}+0.8\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -\frac{12x}{25}-\frac{11x^{2}}{25}+0.8\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -\frac{12x}{25}\mathrm{d}x+\int -\frac{11x^{2}}{25}\mathrm{d}x+\int 0.8\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-\frac{12\int x\mathrm{d}x}{25}-\frac{11\int x^{2}\mathrm{d}x}{25}+\int 0.8\mathrm{d}x$$

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 -0.48 ki te \frac{x^{2}}{2}.

$$-\frac{6x^{2}}{25}-\frac{11\int x^{2}\mathrm{d}x}{25}+\int 0.8\mathrm{d}x$$

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 -0.44 ki te \frac{x^{3}}{3}.

$$-\frac{6x^{2}}{25}-\frac{11x^{3}}{75}+\int 0.8\mathrm{d}x$$

Kimihia te tau tōpū o 0.8 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-\frac{6x^{2}}{25}-\frac{11x^{3}}{75}+\frac{4x}{5}$$

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.

$$-\frac{6}{25}\times 4^{2}-\frac{11}{75}\times 4^{3}+0.8\times 4-\left(-\frac{6}{25}\times 0^{2}-\frac{11}{75}\times 0^{3}+0.8\times 0\right)$$

Whakarūnātia.

$$-\frac{752}{75}$$