Whakaoti i te ∫ (from 0 to 8) of (6.67x-x^2)(-0.083x) wrt x

$$\int_{ 0 }^{ 8 } (6.67x- { x }^{ 2 } )(-0.083x) d x$$

Aromātai

$$-\frac{88976}{9375}\approx -9.490773333$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 6.67x-x^{2} ki te -0.083.

$$\int _{0}^{8}\left(-0.55361x+0.083x^{2}\right)x\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -0.55361x+0.083x^{2} ki te x.

$$\int _{0}^{8}-0.55361x^{2}+0.083x^{3}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -\frac{55361x^{2}}{100000}+\frac{83x^{3}}{1000}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -\frac{55361x^{2}}{100000}\mathrm{d}x+\int \frac{83x^{3}}{1000}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-\frac{55361\int x^{2}\mathrm{d}x}{100000}+\frac{83\int x^{3}\mathrm{d}x}{1000}$$

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 -0.55361 ki te \frac{x^{3}}{3}.

$$-\frac{55361x^{3}}{300000}+\frac{83\int x^{3}\mathrm{d}x}{1000}$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{3}\mathrm{d}x ki te \frac{x^{4}}{4}. Whakareatia 0.083 ki te \frac{x^{4}}{4}.

$$-\frac{55361x^{3}}{300000}+\frac{83x^{4}}{4000}$$

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.

$$-\frac{55361}{300000}\times 8^{3}+\frac{83}{4000}\times 8^{4}-\left(-\frac{55361}{300000}\times 0^{3}+\frac{83}{4000}\times 0^{4}\right)$$

Whakarūnātia.

$$-\frac{88976}{9375}$$