Question

Let f(x) be a continuous function such that the area bounded by the curve y = f(x), x-axis and the lines x = 0 and x = a is `a^2/2 + a/2 sin a + pi/2 cos a`, then `f(pi/2)` =

Options

• 1

• `1/2`

• `1/3`

• None of these

Answer 1

`1/2`

Explanation:

We have, `int_0^a f(x)  dx = a^2/2 + a/2 sin a + pi/2 cos a`

Differentiating w.r.t. a, we get

f(a) = `a + 1/2 (sin a + a cos a) - pi/2 sin a`

Put a = `pi/2 ; f(pi/2) = pi/2 + 1/2 - pi/2 = 1/2`