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Question Number 116437 by ZiYangLee last updated on 04/Oct/20
Provethatπ<227
Answered by floor(10²Eta[1]) last updated on 04/Oct/20
let′slookattheintegralandsolveit: I(x)=∫01x4(1−x)41+x2dx =∫01x8−4x7+6x6−4x5+x41+x2dx =∫01(x6−4x5+5x4−4x2+4−41+x2)dx =[x77−2x63+x5−4x33+4x−4tan−1(x)]01 =227−π andsinceI(x)>0so 227−π>0⇒π<227
Commented byZiYangLee last updated on 04/Oct/20
wow
Answered by MJS_new last updated on 04/Oct/20
theareaofaregularpolygonwithnsides andanincircleofradius1is An=n1−cos2πn1+cos2πn limn→∞An=π[approximatesthecircleobviousbecausethepolygon] if227<π⇒An=227hasnosolution∈R ⇔ifAn=227⇒227>π An=227⇒n≈90.4298 ⇒227>π
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