Whakaoti i te ∫ (from 2 to 7) of left(4112x-2left(x-2right)-x-2/2right)7/23 wrt x

$$\int_{ 2 }^{ 7 } \left( 4112x-2 \left( x-2 \right) - \frac{ x-2 }{ 2 } \right) \frac{ 7 }{ 23 } d x$$

Aromātai

$$\frac{112595}{4}=28148.75$$

Ngā Upane Otinga

Pahekotia te -2\left(x-2\right) me -\frac{x-2}{2}, ka -\frac{5}{2}\left(x-2\right).

$$\int _{2}^{7}\left(4112x-\frac{5}{2}\left(x-2\right)\right)\times \frac{7}{23}\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te -\frac{5}{2} ki te x-2.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x-\frac{5}{2}\left(-2\right)\right)\times \frac{7}{23}\mathrm{d}x$$

Tuhia te -\frac{5}{2}\left(-2\right) hei hautanga kotahi.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+\frac{-5\left(-2\right)}{2}\right)\times \frac{7}{23}\mathrm{d}x$$

Whakareatia te -5 ki te -2, ka 10.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+\frac{10}{2}\right)\times \frac{7}{23}\mathrm{d}x$$

Whakawehea te 10 ki te 2, kia riro ko 5.

$$\int _{2}^{7}\left(4112x-\frac{5}{2}x+5\right)\times \frac{7}{23}\mathrm{d}x$$

Pahekotia te 4112x me -\frac{5}{2}x, ka \frac{8219}{2}x.

$$\int _{2}^{7}\left(\frac{8219}{2}x+5\right)\times \frac{7}{23}\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{8219}{2}x+5 ki te \frac{7}{23}.

$$\int _{2}^{7}\frac{8219}{2}x\times \frac{7}{23}+5\times \frac{7}{23}\mathrm{d}x$$

Me whakarea te \frac{8219}{2} ki te \frac{7}{23} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\int _{2}^{7}\frac{8219\times 7}{2\times 23}x+5\times \frac{7}{23}\mathrm{d}x$$

Mahia ngā whakarea i roto i te hautanga \frac{8219\times 7}{2\times 23}.

$$\int _{2}^{7}\frac{57533}{46}x+5\times \frac{7}{23}\mathrm{d}x$$

Tuhia te 5\times \frac{7}{23} hei hautanga kotahi.

$$\int _{2}^{7}\frac{57533}{46}x+\frac{5\times 7}{23}\mathrm{d}x$$

Whakareatia te 5 ki te 7, ka 35.

$$\int _{2}^{7}\frac{57533}{46}x+\frac{35}{23}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{57533x}{46}+\frac{35}{23}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{57533x}{46}\mathrm{d}x+\int \frac{35}{23}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\frac{57533\int x\mathrm{d}x}{46}+\int \frac{35}{23}\mathrm{d}x$$

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 \frac{57533}{46} ki te \frac{x^{2}}{2}.

$$\frac{57533x^{2}}{92}+\int \frac{35}{23}\mathrm{d}x$$

Kimihia te tau tōpū o \frac{35}{23} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$\frac{57533x^{2}}{92}+\frac{35x}{23}$$

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.

$$\frac{57533}{92}\times 7^{2}+\frac{35}{23}\times 7-\left(\frac{57533}{92}\times 2^{2}+\frac{35}{23}\times 2\right)$$

Whakarūnātia.

$$\frac{112595}{4}$$