Question

If the integral from 0 to pi/2 of sec^2 (x/k) dx = k find k, where 0 <= k <= pi.

Answer 1

k = 2

Explanation:

Integral is [k×tan(x/k]

If its equal to k,

k×tan(x/k) = I

tan(x/k) = 1

x = pi/2 upper limit

x = 0 lower limit

tan(pi/2k) - tan(0) = 1

pi/2k = pi/4

So, k = 2