Question

求解一道高数题，题目看图 谢谢！ ps 答案：3.34

Answer 1

简单计算一下即可，详情如图所示

Answer 2

朋友，你好！详细完整清晰过程rt，希望能帮到你解决问题

Answer 3

∫∫<R>xdA = ∫<0, π/4>dθ∫<2cosθ, 2> rcosθ rdr
= ∫<0, π/4>cosθdθ∫<2cosθ, 2> r^2dr
= (1/3)∫<0, π/4>cosθdθ[r^3]<2cosθ, 2>
= (1/3)∫<0, π/4>cosθ[8-8(cosθ)^3]dθ
= (1/3)∫<0, π/4>[8cosθ-8(cosθ)^4]dθ
= (8/3)[sinθ]<0, π/4> - (1/3)∫<0, π/4>2(1+cos2θ)^2dθ
= 4√2/3 - (1/3)∫<0, π/4>[2+4cos2θ+2(cos2θ)^2]dθ
= 4√2/3 - (1/3)∫<0, π/4>(3+4cos2θ+cos4θ)dθ
= 4√2/3 - (1/3)[3θ+2sin2θ+(1/4)sin4θ]<0, π/4>
= (4√2-2)/3 - π/4