Whakaoti i te ∫ (from 0 to 2) of (54.38x)(18/25x)

$$\int _ { 0 } ^ { 2 } ( 54.38 x ) ( 18 / 25 x )$$

Aromātai

$$104.4096$$

Ngā Upane Otinga

Whakareatia te x ki te x, ka x^{2}.

$$\int _{0}^{2}54.38x^{2}\times \frac{18}{25}\mathrm{d}x$$

Me tahuri ki tau ā-ira 54.38 ki te hautau \frac{5438}{100}. Whakahekea te hautanga \frac{5438}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\int _{0}^{2}\frac{2719}{50}x^{2}\times \frac{18}{25}\mathrm{d}x$$

Me whakarea te \frac{2719}{50} ki te \frac{18}{25} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\int _{0}^{2}\frac{2719\times 18}{50\times 25}x^{2}\mathrm{d}x$$

Mahia ngā whakarea i roto i te hautanga \frac{2719\times 18}{50\times 25}.

$$\int _{0}^{2}\frac{48942}{1250}x^{2}\mathrm{d}x$$

Whakahekea te hautanga \frac{48942}{1250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\int _{0}^{2}\frac{24471}{625}x^{2}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{24471x^{2}}{625}\mathrm{d}x$$

Whakatauwehetia te pūmau mā te whakamahi i te \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$\frac{24471\int x^{2}\mathrm{d}x}{625}$$

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}.

$$\frac{8157x^{3}}{625}$$

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.

$$\frac{8157}{625}\times 2^{3}-\frac{8157}{625}\times 0^{3}$$

Whakarūnātia.

$$\frac{65256}{625}$$