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 / 2
x = 0 = 2 sin t => sin t = 0 => t = 0
A smarter method using Analytic Geometry: A circle of radius 2 is