Whakaoti i te ∫ (from 1 to 3) of (3x^3-2x+5) wrt x

$$\int_{ 1 }^{ 3 } (3 { x }^{ 3 } -2x+5) d x$$

Aromātai

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Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 3x^{3}-2x+5\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 3x^{3}\mathrm{d}x+\int -2x\mathrm{d}x+\int 5\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$3\int x^{3}\mathrm{d}x-2\int x\mathrm{d}x+\int 5\mathrm{d}x$$

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

$$\frac{3x^{4}}{4}-2\int x\mathrm{d}x+\int 5\mathrm{d}x$$

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

$$\frac{3x^{4}}{4}-x^{2}+\int 5\mathrm{d}x$$

Kimihia te tau tōpū o 5 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{3x^{4}}{4}-x^{2}+5x$$

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.

$$\frac{3}{4}\times 3^{4}-3^{2}+5\times 3-\left(\frac{3}{4}\times 1^{4}-1^{2}+5\times 1\right)$$

Whakarūnātia.

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