Whakaoti i te ∫ (from 1 to 100) of 4/x^3

$$\int _ { 1 } ^ { 100 } \frac { 4 } { x ^ { 3 } }$$

Aromātai

$$\frac{9999}{5000}=1.9998$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{4}{x^{3}}\mathrm{d}x$$

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.

$$4\int \frac{1}{x^{3}}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int \frac{1}{x^{3}}\mathrm{d}x ki te -\frac{1}{2x^{2}}. Whakareatia 4 ki te -\frac{1}{2x^{2}}.

$$-\frac{2}{x^{2}}$$

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.

$$-2\times 100^{-2}+2\times 1^{-2}$$

Whakarūnātia.

$$\frac{9999}{5000}$$