Whakaoti i te ∫ (from 0 to 3) of (13.5+9.5x)(6+x) wrt x

$$\int_{ 0 }^{ 3 } (13.5+9.5x)(6+x) d x$$

Aromātai

$$645.75$$

Ngā Upane Otinga

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 13.5+9.5x ki ia tau o 6+x.

$$\int _{0}^{3}81+13.5x+57x+9.5x^{2}\mathrm{d}x$$

Pahekotia te 13.5x me 57x, ka 70.5x.

$$\int _{0}^{3}81+70.5x+9.5x^{2}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 81+\frac{141x}{2}+\frac{19x^{2}}{2}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 81\mathrm{d}x+\int \frac{141x}{2}\mathrm{d}x+\int \frac{19x^{2}}{2}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 81\mathrm{d}x+\frac{141\int x\mathrm{d}x}{2}+\frac{19\int x^{2}\mathrm{d}x}{2}$$

Kimihia te tau tōpū o 81 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$81x+\frac{141\int x\mathrm{d}x}{2}+\frac{19\int x^{2}\mathrm{d}x}{2}$$

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 70.5 ki te \frac{x^{2}}{2}.

$$81x+\frac{141x^{2}}{4}+\frac{19\int x^{2}\mathrm{d}x}{2}$$

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 9.5 ki te \frac{x^{3}}{3}.

$$81x+\frac{141x^{2}}{4}+\frac{19x^{3}}{6}$$

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.

$$81\times 3+\frac{141}{4}\times 3^{2}+\frac{19}{6}\times 3^{3}-\left(81\times 0+\frac{141}{4}\times 0^{2}+\frac{19}{6}\times 0^{3}\right)$$

Whakarūnātia.

$$\frac{2583}{4}$$