Question

How do you evaluate the definite integral `int sec^2t dt` from [-pi/4, pi/4]?

Answer 1

Use the rule `intsec^2(x)dx=tan(x)+C`:

`int_(-pi/4)^(pi/4)sec^2(t)dt=tan(t)|_(-pi/4)^(pi/4)=tan(pi/4)-tan(-pi/4)=2`