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Question Number 126997 by bramlexs22 last updated on 26/Dec/20
∫10arcsin(sinx2)dx=?
Answered by Evimene last updated on 26/Dec/20
solutionlet2=αf(α)=∫01arcsin(sinxα)dx⇔differentiatingαf′(α)=∫01α2α2−sin2xdx⇔multiplybysec2xsec2xf′(α)=∫01α2sec2xα2sec2x−α2tan2xdx⇔recallsec2x+tan2x=1f′(α)=∫01sec2xdx;⇔[tanx]01f1(α)=π4f(α)=π4x+c⇔f(0)=0;soc=0f(α)=π4cadetpraise
Commented by bramlexs22 last updated on 26/Dec/20
Feynmannmethod?
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