the integral is from 0 to π/4:
(1 + tanθ)^3(sec^2θ)dθ
So, here's what I did:
u = 1 + tanθ
du = sec^2θdθ
so,
(u)^3du
then, I changed the integral limits because I think I'm supposed to (not sure?)
1 + tanθ(π/4) = 2
1 + tanθ(0) = 1
so,
1/4(u)^4
then I simply plugged the new limit numbers into the equation to finish it
[1/4(2)^4] - [1/4(1)^4] = 15/4
Did I do it right?
Execellent!
You could eitherthen, I changed the integral limits because I think I'm supposed to (not sure?)
1) Do the integral in terms of u, then write the answer in terms of again and evaluate between the limits of the original integral.
2) change the limits of integration to values of u and then evaluate the between those limits.
In my opinion, it is better and easier to do (2) as you do here.
Of course, you do NOT use the " " values with the "u" variable!
1 + tanθ(π/4) = 2
1 + tanθ(0) = 1
so,
1/4(u)^4
then I simply plugged the new limit numbers into the equation to finish it
[1/4(2)^4] - [1/4(1)^4] = 15/4
Did I do it right?