Find G(1) and G'(pi/5).

Question

G(x)= 1∫x (tan t) dt

Answer 1

Find the integral of tant from t=x to t=1.

 

∫tant = ln(sect)

 

 

Then,

 

G(x) = ln(sec(1)) - ln(sec(x))

 

G(1) = 0

 

 

G'(x) = -tant

 

G'(π/5) = -tan(π/5)