定积分0到负3x+1/根号下x+4dx

Question

定积分0到负3 x+1/根号下x+4 dx

Answer 1

令t=(x+1)^(1/2)所以x=t^2-1所以dx=2tdt当x=0,t=1,x=2,t=3^(1/2)原式=∫2tdt/(t+t^3)].上限3^(1/2).下限1=2∫dt/(1+t^2)=2[arctant].上限3^(1/2).下限1=2[arctan3^(1/2)-arctan1]=2(π/3-π/4)=π/6...