1.23: Equation of a curve from a trigonometric second derivative

0606/11/O/N/19 — Question 12 · 8 marks

A curve is such that d2ydx2=2sin(x+π3)\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}} = 2\sin\left(x + \dfrac{\pi}{3}\right). Given that the curve has a gradient of 55 at the point (π3,5π3)\left(\dfrac{\pi}{3}, \dfrac{5\pi}{3}\right), find the equation of the curve.
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