Question

Question B: The following integral is important in a particular geometry problem

(you will learn later which geometry problem):

integral of sqrt( a^2 * cos(t) + b^2 * sin(t) ) dt from t=0 to t=2pi.

For each of the following methods, write down what happens as you try it, but don't spend very long on it.

i) Try a simple u-substitution.

ii) Try integration by parts.

iii) Try trig substitution.

iv) Any other ideas?

v) optional: what if b=a? Can you simplify it and solve it?

Answer 1