Suppose that INT{pi to t} g(u)du= e^(cos(t)). Show that INT{0 to t}g(u)du= e^(cos(t))- e.
I have no idea how to prove. Tried taking derivative of the result, but didn't think that would help with anything.
e^cos t = value at t - value at pi
= value at t - e^cos pi
but cos pi = -1
so
e^cos t = value at t -e^-1
or
e^cos t = value at t - 1/e
so
value at t = 1/e + e^cos t
-------------------
now do value at t - value at 0
value at 0 = 1/e + e^1
= 1/e + e
value at t = 1/e + e^cos t
subtract
1/e + e^cos t - 1/e - e
= e^cos t - e
whew :)