f(x)=(x+1)/(1+x^2)

Question

a) explain why the graph lies above the x axis on the interval x=0 and x=sqrt(3)

b)write an expression using the indefinite integral that gives the area between the graph f and the x axis between the values x=0 and x=sqrt(3).

c)use integration to find the area described in b)

Answer 1

for x > -1, both numerator and denominator are positive.

∫[0,√3] (x+1)/(1+x^2) dx = π/3 + ln(2)

Good luck on this one if you haven't yet studied trig substitutions.