Question

Find a function f and a value of the constant a such that 2`int_a^xf(t)dt=2sinx-1` ?

Answer 1

• `f(x) = cos x`

• `a = pi/6`

Explanation:

`2 int_a^xf(t)dt=2sinx-1`

Differentiate wrt x, using Liebnitz Integral Rule for LHS:

`2 f(x) =2cosx, qquad :. f(x) = cos x`

Then integrate LHS:

`2 int_a^x cos t \ dt=2 [sint]_a^x = 2 sin x - 2 sin a`

• `implies a = pi/6`