| 2005/09/03(Sat) 17:04:57 編集(投稿者)
I (4)=∫[0、π/2」cos^4xdx =∫[0、π/2」cosx cos^3xdx 部分積分スルト =[sinx cos^3x](0、π/2)−∫[0、π/2」sinx (3cos^2x) (- sinx) dx =3∫[0、π/2」sin^2x cos^2xdx =3∫[0、π/2」(1−cos^2x)cos^2xdx=3{∫[0、π/2」cos^2xdx−I (4)} I (4)=3{∫[0、π/2」cos^2xdx−I (4)} I (4)=3/4∫[0、π/2」cos^2xdx I (2)=∫[0、π/2」cos^2xdx =∫[0、π/2」cosx cosx dx =[sinx cosx] (0、π/2)−∫[0、π/2」sinx (- sinx) dx =∫[0、π/2」sin^2x dx =∫[0、π/2」(1−cos^2x) dx=∫[0、π/2」1dx−I (2) よって I (2)=∫[0、π/2」1dx−I (2) 2・I (2)=∫[0、π/2」1dx=π/2 I (2)=(1/2) (π/2) I (4)=(3/4) I (2)=(3/4) (1/2) (π/2) ∫^{パイ/2}_0cos^3xdx も同様ニデキマス。
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