A curve is such that $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=4\cos2x$. The gradient of the curv

Question

A curve is such that $\dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=4\cos2x$. The gradient of the curve when $x=0$ is $1$, and the curve passes through $\left(\dfrac{\pi}{4},2\right)$. Find the equation of the curve.[7]

Accepted Answer

$y=-\cos2x+x+2-\dfrac{\pi}{4}$

Trigonometric curve from a second derivative

Trigonometric curve from a second derivative

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