Question

高数定积分积分上限1,下限0,被积为x平方/根号(4-X平方),

Answer 1

换元：x＝2sint,x＝0时,t＝0,x＝1时,t＝π/6

∫(0～1)x^2/√(4-x^2)dx＝∫(0～π/6) 4(sint)^2dt＝∫(0～π/6) (2－2cos(2t))dt,被积函数的原函数是2t－sin(2t),结果是π/3－√3/2