Question

计算二重积分：∫∫x（根号下y）dσ,其中D是由两条抛物线y=根号下x及y=x2所围成的闭区域！！求过程！

答案：6/55，求过程！！

Answer 1

{ y = √x
{ y = x²
==>交点为(0，0)，(1，1)
∫∫_D x√y dσ
= ∫(0→1) x ∫(x²→√x) √y dy
= ∫(0→1) x · (2/3)y^(3/2)：(x²→√x) dx
= ∫(0→1) (2/3)x · [(√x)^(3/2) - (x²)^(3/2)] dx
= ∫(0→1) [(2/3)x^(7/4) - (2/3)x⁴] dx
= [(2/3)(4/11)x^(11/4) - (2/3)(1/5)x⁵]：(0→1)
= (8/33) - (2/15)
= 6/55

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Answer 2

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Answer 3

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