Whakaoti i te ∫ (from 0 to 2) of 54.38x7/25x wrt x

$$\int_{ 0 }^{ 2 } 54.38x \frac{ 7 }{ 25 } x d x$$

Aromātai

$$\frac{76132}{1875}\approx 40.603733333$$

Ngā Upane Otinga

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

$$\int _{0}^{2}54.38x^{2}\times \frac{7}{25}\mathrm{d}x$$

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.

$$\int _{0}^{2}\frac{2719}{50}x^{2}\times \frac{7}{25}\mathrm{d}x$$

Me whakarea te \frac{2719}{50} ki te \frac{7}{25} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\int _{0}^{2}\frac{2719\times 7}{50\times 25}x^{2}\mathrm{d}x$$

Mahia ngā whakarea i roto i te hautanga \frac{2719\times 7}{50\times 25}.

$$\int _{0}^{2}\frac{19033}{1250}x^{2}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{19033x^{2}}{1250}\mathrm{d}x$$

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.

$$\frac{19033\int x^{2}\mathrm{d}x}{1250}$$

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}.

$$\frac{19033x^{3}}{3750}$$

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.

$$\frac{19033}{3750}\times 2^{3}-\frac{19033}{3750}\times 0^{3}$$

Whakarūnātia.

$$\frac{76132}{1875}$$