根下1+x^2从0到1积分该怎么算的啊,
问题描述:
根下1+x^2从0到1积分该怎么算的啊,
答
∫[0,1]√(1+x^2)dx=x√(1+x^2)|[0,1]-∫[0,1]x^2dx/√(1+x^2)=√2-∫[0,1]√(1+x^2)dx+∫[0,1]dx/√(1+x^2)2∫[0,1]√(1+x^2)dx=√2+∫[0,1]dx/√(1+x^2)∫[0,1]√(1+x^2)dx=√2/2+(1/2)ln(√2+1)x=tanu x=0,u=0,x=...