Whakaoti i te ∫ (from 0 to 2) of x(3+2x) wrt x

$$\int _ { 0 } ^ { 2 } x ( 3 + 2 x ) d x$$

Aromātai

$$\frac{34}{3}\approx 11.333333333$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 3+2x.

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

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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

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

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

$$\frac{3x^{2}}{2}+\frac{2x^{3}}{3}$$

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.

$$\frac{3}{2}\times 2^{2}+\frac{2}{3}\times 2^{3}-\left(\frac{3}{2}\times 0^{2}+\frac{2}{3}\times 0^{3}\right)$$

Whakarūnātia.

$$\frac{34}{3}$$