x2=byyx2=ayy2=qxy^2=px0图10.14设D是由四条抛物线 y^2=px , y^2=qx x^2=ay , x^2=by(0pq,0 ab)所围成的区域(图10.14).计算D的面积和二重积分A=∫_0^x1/(xy)dxdy 答案 解引入参数u,v,使得y2=ux, x^2=vy ,其中 p≤u≤q , a≤v≤b .这说明,在这种变换之下,图形D变...
【答案】:4个函数都是奇函数,所围成的区域关于原点对称,计算在第一象限的部分面积,再乘以2.x>0时y=a/x与y=px交于点A(√(a/p),√(ap)),与y=qx交于点B(√(a/q),√(aq));y=b/x与y=px交于点D(√(b/p),√(bp)),与y=qx交于点C(√(b/q),√(bq)).由0<a<b,0<...
6、曲线。4)几种常见的微分方程1、可分离变量的微分方程一般形式形式:y=f(x,y)对称形式:p(x,y)dx+q(x,y)dy=0(x,y都可以看做函数,另一个为自变量)即:字=-忖(q(x,yh0)或=-铝(p(x,y)M0)dxqx,ydypx,y可分离变量:如果一阶微分方程能写成g(y)dy=f(x)dx的形式。特点:一端只含y的函数和...
(px+qy)²=p²x²+2pqxy+q²y²(p²+q²)(x²+y²)=p²x²+p²y²+q²x²+q²y²因为0≤(py-qx)²所以2pqxy≤p²y²+q²x²所以p²x²+2p...
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,√(aq));y=b/x与y=px交于点D(√(b/p),√(bp)),与y=qx交于点C(√(b/q),√(bq)).由0<a<b,0<p<q,无法确定xA,xC的大小,需讨论。2)作曲线坐标变换:xy=u,y/x=v,计算雅可比行列式,J=2/v,∴所求面积=2∫<a,b>du∫<p,q>2dv/v=4(b-a)ln(q/p).仅供参考。
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