化簡無理式和求定積分問題

(a) 1/√(7+4√3)
=1/√(7+2√12)
=1/√(4+2√12+3)
=1/(2+√3)
=2－√3

(b) ∫(0 to 2)_dx/√(16－x^2)
Set x=4Sinw
dx=4Coswdw
16－x^2=16－16Sin^2 w=16Cos^2 w
∫(0 to 2)_dx/√(16－x^2)
=∫(0 to π/3)_4Coswdw/4Cosw
=∫(0 to π/3)_dw
=π/3