- 171 名前：イナ mailto:sage [2022/11/07(月) 23:58:32.19 ID:CoO3DO9r.net]
- 前>>123
>>30
x=sintとおくとdx=costdt
∫[x=0→1]x^2√(1-x^2)dx=∫[t=0→π/2]sin^2tcos^2tdt
=∫[t=0→π/2]｛(1-cos2t)/2｝｛(1+cos2t)/2｝dt
=∫[t=0→π/2][｛1-cos^2(2t)｝/4]dt
=∫[t=0→π/2](1/4-1/8-cos4t/8)dt
=∫[t=0→π/2](1/8-cos4t/8)dt
=[t=0→π/2][t/8-sin4t/32]
=π/16
これ、あってんの？
