∫(2+x^2013)√(4-x^2)dx
=∫2√(4-x^2)dx+∫x^2013√(4-x^2)dx
=∫2√(4-x^2)dx
令x=2sint,则dx=2costdt
原式=∫(-π/2,π/2)2*2cost*2costdt
=4∫(-π/2,π/2)(1+cos2t)dt
=4(t+0.5sin2t)|(-π/2,π/2)
=4π
求定积分 (2+x^2013)根号（4-x^2)dx -2积到2
∫(2+x^2013)√(4-x^2)dx
=∫2√(4-x^2)dx+∫x^2013√(4-x^2)dx
=∫2√(4-x^2)dx
令x=2sint,则dx=2costdt
原式=∫(-π/2,π/2)2*2cost*2costdt
=4∫(-π/2,π/2)(1+cos2t)dt
=4(t+0.5sin2t)|(-π/2,π/2)
=4π