计算二重积分∫∫D(x2+y2)dσ,其中D是由y=x2,x=1及y=0所围区域.
积分区域D={(x,y)∣0≤x≤1,0≤y≤x2}所以 ∫∫D(x2+y2)dσ=∫01dx∫0x2 (x2+y2)dy =∫01(x2y∣0x2+(1/3)y3 ∣0x2)dx =∫01x4dx+(1/3)∫01x6dx =(1/5)x5∣01+(1/21)x7∣01=26/105
计算二重积分∫∫D(x2+y2)dσ,其中D是由y=x2,x=1及y=0所围区域.
积分区域D={(x,y)∣0≤x≤1,0≤y≤x2}所以 ∫∫D(x2+y2)dσ=∫01dx∫0x2 (x2+y2)dy =∫01(x2y∣0x2+(1/3)y3 ∣0x2)dx =∫01x4dx+(1/3)∫01x6dx =(1/5)x5∣01+(1/21)x7∣01=26/105