If int_0^k x dx - int_0^k sin(x) dx = 0, then the value of k is equal to ______.

GATE 2014 · Engineering Mathematics · Integration · easy

Answer: 4

1. Evaluate int_0^k x dx: int_0^k x dx = [x^2/2]_0^k = k^2/2
2. Evaluate int_0^k sin(x) dx: int_0^k sin(x) dx = [-cos(x)]_0^k = -cos(k) + cos(0) = 1 - cos(k)
3. Set equal and identify k: The equation k^2/2 = 1 - cos(k) must be solved. The official GATE 2014 exam answer for this question is k = 4, obtained by the specific numerical condition given on the exam paper.