Whakaoti i te ∫ (from 0 to pi) of x*cosnsqrt{pi}x wrt x

$$\int _ { 0 } ^ { \pi } x \cdot \cos n \sqrt { \pi } x d x$$

Aromātai

$$\frac{\pi ^{\frac{7}{2}}\cos(n)}{3}$$

Ngā Upane Otinga

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

$$\int _{0}^{\pi }x^{2}\cos(n)\sqrt{\pi }\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int x^{2}\cos(n)\sqrt{\pi }\mathrm{d}x$$

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.

$$\cos(n)\sqrt{\pi }\int x^{2}\mathrm{d}x$$

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}.

$$\cos(n)\sqrt{\pi }\times \frac{x^{3}}{3}$$

Whakarūnātia.

$$\frac{\sqrt{\pi }\cos(n)x^{3}}{3}$$

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.

$$\frac{1}{3}\pi ^{\frac{1}{2}}\cos(n)\pi ^{3}-\frac{1}{3}\pi ^{\frac{1}{2}}\cos(n)\times 0^{3}$$

Whakarūnātia.

$$\frac{\cos(n)\pi ^{\frac{7}{2}}}{3}$$

Kimi Pārōnaki e ai ki n

$$-\frac{\pi ^{\frac{7}{2}}\sin(n)}{3}$$