Pythagorean identities will just have to do

Calculus Level 4

E=0π/21sin(2016x)dx\mathscr{E} = \displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(2016 x) }\, dx

Find E.\mathscr{E}.


Inspiration

Bonus: Generalize for 0π/21sin(12nx)dx \displaystyle \int_{0}^{\pi/2} \sqrt{1- \sin(12n x) }\, dx , where nn is a positive integer, and prove it.

×

Problem Loading...

Note Loading...

Set Loading...