Question

The area bounded by the curve y = f(x), X-axis and ordinates x = 1 and x = a is (a - 1) cos(2a + 7), then f(x) is ______.

Options

• 2(1 - x) sin(2x + 7) + cos(2x + 7)

• (a - 1)sin (2x + 7) + 2cos(2x + 7)

• (1 - a)cos (2x + 7) + 3sin(2x + 7)

• 2(x - 1) cos(2x + 7) + sin(2x + 7)

Answer 1

The area bounded by the curve y = f(x), X-axis and ordinates x = 1 and x = a is (a - 1) cos(2a + 7), then f(x) is 2(1 - x) sin(2x + 7) + cos(2x + 7).

Explanation:

According to the given condition,

`int_1^"a" f(x) dx = (a - 1) cos(2a + 7)`

Differentiating w.r.t. a, we get

f(a).1 = -2(a - 1) sin(2a + 7) + cos(2a + 7)

∴ f(x) = 2(1 - x) sin(2x + 7) + cos(2x + 7)