Whakaoti i te ∫ (from 0 to 1) of 2^x+x^2 wrt x

$$\int _ { 0 } ^ { 1 } 2 ^ { x } + x ^ { 2 } d x$$

Aromātai

$$\frac{1}{\ln(2)}+\frac{1}{3}\approx 1.776028374$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakamahia te \int x^{k}\mathrm{d}k=\frac{x^{k}}{\ln(x)} mai i te ripanga o ngā tau tōpū pātahi kia whakaputa i te huanga.

$$\frac{2^{x}}{\ln(2)}+\int x^{2}\mathrm{d}x$$

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}.

$$\frac{2^{x}}{\ln(2)}+\frac{x^{3}}{3}$$

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.

$$2^{1}\ln(2)^{-1}+\frac{1^{3}}{3}-\left(2^{0}\ln(2)^{-1}+\frac{0^{3}}{3}\right)$$

Whakarūnātia.

$$\frac{1}{3}+\frac{1}{\ln(2)}$$