China 南京航空航天大学 Nanjing University of Aeronautics and Astronautics set the WiFi password as the answer of this integral (first 6 digits).

Can you solve it?

*(If can’t, please revise GCE “A-level” / Baccalaureate / 高考 Calculus* *微积分*)

**Answer** : Break the integral (I) into 2 parts:

I = A(x) + B(x)

**A(x) = – A(-x) => Odd function **

=> **A(x) = 0** since its area canceled out over [-2, 2]

**B(x) = B(-x) => Even function**

Let x = 2 sin t => dx = 2 cos t. dt

x = 2 = 2 sin t => sin t = 1 =>

t =π/ 2x = 0 = 2 sin t => sin t = 0 =>

t = 0

A smarter method using Analytic Geometry: A circle of radius 2 is