Whakaoti i te ∫ (from 0 to 3) of (5x-3)^2 wrt x=

$$\int _ { 0 } ^ { 3 } ( 5 x - 3 ) ^ { 2 } d x =$$

Aromātai

$$117$$

Ngā Upane Otinga

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(5x-3\right)^{2}.

$$\int _{0}^{3}25x^{2}-30x+9\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 25x^{2}-30x+9\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 25x^{2}\mathrm{d}x+\int -30x\mathrm{d}x+\int 9\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$25\int x^{2}\mathrm{d}x-30\int x\mathrm{d}x+\int 9\mathrm{d}x$$

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

$$\frac{25x^{3}}{3}-30\int x\mathrm{d}x+\int 9\mathrm{d}x$$

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 -30 ki te \frac{x^{2}}{2}.

$$\frac{25x^{3}}{3}-15x^{2}+\int 9\mathrm{d}x$$

Kimihia te tau tōpū o 9 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{25x^{3}}{3}-15x^{2}+9x$$

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.

$$\frac{25}{3}\times 3^{3}-15\times 3^{2}+9\times 3-\left(\frac{25}{3}\times 0^{3}-15\times 0^{2}+9\times 0\right)$$

Whakarūnātia.

$$117$$