计算下列曲面所围立体的体积 z = x^2+y^2, z = 2x^2+2y^2, y =x, y = x^2

怎么算啊?不知道怎么列式子
2025-04-04 10:51:18
推荐回答(2个)
回答1:

∫∫∫dv
=∫∫dxdy∫(x²+y²→2x²+2y²) dz
=∫∫dxdy z |(x²+y²→2x²+2y²)
=∫∫dxdy (x²+y²)
=∫(0→1) dx ∫(x²→x) (x²+y²) dy
=∫(0→1) dx (x²y + y³/3) |(x²→x)
=∫(0→1) (4x³/3 - x^4 - x^6/3) dx
=(x^4/3 - x^5/5 - x^7/21) |(0→1)
=1/3 - 1/5 -1/21
=自己化简下

回答2:

题目是完整的吗,没有上限和下限