椭圆的面积公式如何求解椭圆面积及椭圆面积公式?

用定积分设椭圆的方程为x^2/a^2+y^2/b^2=1椭圆是以原点对称只需计算第一象限的面积乘4倍椭圆面积=S第一象限y=b(1-x^2/a^2)^0。5x由0到aS/4=∫(0 a)b(1-x^2/a^2)^0。5dx 令 x/a=sint t=arcsin(x/a) x=asint x=0 t=0x=a t=π/2=∫(0 π/2)b(1-(sint)^2)^0。5d(asint)=ab∫(0 π/2)(cost)^2dt=ab∫(0 π/2)(cost)^2-1/2+1/2dt=ab/4∫(0 π/2)cos(2t)+1d2t=ab/4(sin(2t)+2t)|(0 π/2)=ab/4(sin(2*π/2)+2*π/2-sin(2*0)+2*0)=abπ/4S=abπ