Question

Hello, I am struggling to draw this graph of function defined by integrals, can someone please explain how using a step by step method and clear hand writing?

3. Let Si(a) j sinfol dt (a) Show that the function Si(x) is increasing at x =-π/2. (b) IsT a stationary point of Si(x)? Justify your claim (c) Given that Si(0) 0, sketch Si() in the region 0 s z 3 3m (a sketch ofican be found in the sin (x can bc found in the Problem Sheet section of Blackboard)

Answer 1

"Sin (x) = integral^x_0 sin t/t dt to show that si(x) is increasing at x = -pi/2 d/dx (si (x)) = integral^x_0 partial differential/partial differential x (sint/t) dt + sin (x)/x 1 - 0 = sin x/x using Leibanitz role for integration d/dx (si (x))/pi/2 = -1/- pi/2 = 2/pi > 0 since derivative is +ve f^1 si(x) is increasing x = pi a stationary d/dx (si (x)) = sin x/x