高数，答案是二分之π，求过程。要用换元法，已知开头是令X=√2Sint。求接下来的过程，不要画图，

Question

如题所述

Answer 1

解：
令x=√2sint
x：0→√2，x/√2：0→1
sint：0→1
t：0→π/2

∫[0：√2]√(2-x²)dx
=√2∫[0：√2]√[1-(x/√2)²]dx
=2∫[0：√2]√[1-(x/√2)²]d(x/√2)
=2∫[0：π/2]√(1-sin²t)d(sint)
=2∫[0：π/2]|cost|·costdt
=∫[0：π/2]2cos²tdt
=∫[0：π/2][1+cos(2t)]dt
=∫[0：π/2]dt+½∫[0：π/2]cos(2t)d(2t)
=t|[0：π/2] +½sin(2t)|[0：π/2]
=π/2-0+½(sinπ-sin0)
=π/2本回答被提问者采纳

Answer 2