Whakaoti i te ∫ (from 0.50 to 1.00) of (52.8x+38.4x^2) wrt x

$$\int _ { 0.50 } ^ { 1.00 } ( 52.8 x + 38.4 x ^ { 2 } ) d x$$

Aromātai

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Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{264x+192x^{2}}{5}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{264x}{5}\mathrm{d}x+\int \frac{192x^{2}}{5}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\frac{264\int x\mathrm{d}x+192\int x^{2}\mathrm{d}x}{5}$$

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

$$\frac{132x^{2}+192\int x^{2}\mathrm{d}x}{5}$$

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

$$\frac{132x^{2}+64x^{3}}{5}$$

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.

$$\frac{132}{5}\times 1^{2}+\frac{64}{5}\times 1^{3}-\left(\frac{132}{5}\times 0.5^{2}+\frac{64}{5}\times 0.5^{3}\right)$$

Whakarūnātia.

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