二重积分,要画图
1个回答

(1) ∫[0,1]dy∫[y,1]e^xdx

=∫[0,1](e-e^y)dy

=e-e^y[0,1]

=1

(2) 原式=∫[0,π/2]dθ∫[0,1]ρ^4sin^2(θ)cosθdρ

=∫[0,π/2]sin^2(θ)cosθdθ∫[0,1]ρ^4dρ

=1/3sin^3(θ)[0,π/2]*1/5ρ^5[0,1]

=1/15

(3) 此题有问题区域不封闭

(4) 原式=∫[0,2π]dθ∫[0,2]ρ(4-ρ^2)dρ

=2π*(2ρ^2-1/4ρ^4)[0,2]

=2π*(8-4)

=8π

(5) 原式=∫[0,π]dx∫[x^2,πx]sinx/xdy

=∫[0,π]sinx/x(πx-x^2)dx

=π∫[0,π]sinxdx- ∫[0,π]xsinxdx

=-πcosx[0,π]+ xcosx[0,π]-π∫[0,π]cosxdx

=2π-π

=π

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