If f(x) is a non-negative continuous function such that the area bounded by the curve y = f(x), X-axis and the ordinates x = pi/4 and x = β > pi/4 is ( β sin β + pi/4 cos β + √2). Then, f(pi/2) is equal to
(a) (1 - pi/4 + √2)
(b) (1 - pi/4 - √2)
(c) (pi/4 - √2 + 1)
(d) (pi/4 + √2 -1)
Correct option (a) (1 - pi/4 + √2)
Explanation:
According to the given condition,
On differentiating both sides w.r.t, B, we get
