Whakaoti i te ∫ (from 0 to 3) of (91x+198)(-6-x) wrt x

$$\int_{ 0 }^{ 3 } (91x+198)(-6-x) d x$$

Aromātai

$$-7731$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 91x+198 ki ia tau o -6-x.

$$\int _{0}^{3}-546x-91x^{2}-1188-198x\mathrm{d}x$$

Pahekotia te -546x me -198x, ka -744x.

$$\int _{0}^{3}-744x-91x^{2}-1188\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -744x-91x^{2}-1188\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -744x\mathrm{d}x+\int -91x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-744\int x\mathrm{d}x-91\int x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

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 -744 ki te \frac{x^{2}}{2}.

$$-372x^{2}-91\int x^{2}\mathrm{d}x+\int -1188\mathrm{d}x$$

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 -91 ki te \frac{x^{3}}{3}.

$$-372x^{2}-\frac{91x^{3}}{3}+\int -1188\mathrm{d}x$$

Kimihia te tau tōpū o -1188 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-372x^{2}-\frac{91x^{3}}{3}-1188x$$

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.

$$-372\times 3^{2}-\frac{91}{3}\times 3^{3}-1188\times 3-\left(-372\times 0^{2}-\frac{91}{3}\times 0^{3}-1188\times 0\right)$$

Whakarūnātia.

$$-7731$$