Question

若f(x)= ∫(x,0)1/(1+t^2)+∫(1/x,0)1/(1+t^2),则f(x)=?

Answer 1

f(x) = ∫(0-->x) 1/(1 + t²) dt + ∫(0-->1/x) 1/(1 + t²) dt
= arctan(x) + arctan(1/x)
= arctan(x) + arccot(x)
= π/2

追问

arccot(x)怎么算的还有就是arctan(x) + arccot(x)
= π/2 怎么到的

追答

倒数参数关系
arctan(1/x) = π/2 - arctan(x) = arccot(x)，前提是x > 0
==> π/2 - arctan(x) = arccot(x)
==> arctan(x) + arccot(x) = π/2

Answer 2

0

追问

不对,是π/2