moi nguoi oi giup minh bai tich phan nay voi

N

nguyenbahiep1

cmr:
tich phan can tu 0 den pi cua xf(sin x)dx = pi/2 tich phan can tu 0 dan pi cua f(sin x)dx
Bấm để xem đầy đủ nội dung ...

[laTEX]I = \int_{0}^{\pi}xf(sinx)dx \\ \\ x= \pi- t \Rightarrow dx = - dt \\ \\ I = \int_{0}^{\pi}(\pi-t)f(sin(\pi-t))dt \\ \\ I = \int_{0}^{\pi}(\pi-t)f(sint)dt \\ \\ I = \pi.\int_{0}^{\pi}f(sint)dt - \int_{0}^{\pi}t.f(sint).dt \\ \\ I = \pi.\int_{0}^{\pi}f(sint)dt - I \\ \\ 2I = \pi.\int_{0}^{\pi}f(sint)dt = \pi.\int_{0}^{\pi}f(sinx)dx \\ \\ I = \frac{\pi}{2}\int_{0}^{\pi}f(sin x)dx \Rightarrow dpcm[/laTEX]
 
You must log in or register to reply here.
Top Bottom