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Today, $20$:$30$$\newline$Figure $6$$\newline$Figure $6$ shows a sketch of the curve $\newline$$C$ with parametric equations$\newline$$x=8\sin^{2}t \quad y=2\sin 2t+3\sin t \quad0 \leq t \leq \frac{\pi}{2}$$\newline$The region $\newline$$R$, shown shaded in Figure $6$, is bounded by $\newline$$C$, the $\newline$$x$-axis and the line with equation $\newline$$x=4$$\newline$(a) Show that the area of $\newline$$R$ is given by$\newline$$\int_{0}^{a}(8-8\cos 4t+48\sin^{2}t \cos t)dt$$\newline$where $\newline$$a$ is a constant to be found.$\newline$(b) Hence, using algebraic integration, find the exact area of $\newline$$R$.$\newline$($4$)$\newline$Ndokumbirawo help apo