3,y=π/4+㏑(cosx)
y'=(1/cosx)*(-sinx)=-tanx
y''=-1/cos²x=-sec²x
∴y''|x=1 =-sec²1
4,㏑y=㏑(x^x)=x㏑x
那么㏑y^(y)=y㏑y=x^(x)*x㏑x=x^(x+1)*㏑x
所以y^y=e^[x^(x+1)*㏑x]=x^[x^(x+1)]
5,令x=asint,那么dx=acost dt
所以∫√(a²-x²) dx=∫ acost*acost dt
=a²∫cos²t dt
=a²∫(1+cos2t)/2 dt
=a²/2*[∫1 dt＋1/2*∫cos2t d(2t)]
=a²/2*(t＋sin2t)＋C
=a²/2*{arcsin(x/a)＋[x√(a²-x²)]/a²}＋C
=a²/2*arcsin(x/a)＋x/2*√(a²-x²)＋C
那么原式=a²/2*π/2＋0－0－a²/2
=πa²/4－a²/2