$()$USTION $5$

$5\mathrm{.}1$ Evaluate ${\displaystyle \underset{0}{\overset{n}{}}}(3cos3x)dx.$

$5\mathrm{.}2$ Simplify ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2\sqrt[\phantom{2}]{x}+4x)(\sqrt[3]{x}-x^{-1})dx.$

$5\mathrm{.}35\mathrm{.}3\mathrm{.}1$ Sketch the graphs of $y=x^2$ and $y=x+2,$ calculate the points of intersection and show the area to be calculated and the strip to be used.

$5\mathrm{.}3\mathrm{.}2$ Determine the area bounded by the two graphs in QUESTION $5\mathrm{.}3\mathrm{.}1$ with the aid of integration.

$5\mathrm{.}4$ Simplify ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{co{s}^{2}x+si{n}^{2}x}{si{n}^{2}x})$

TOTAL: $,100$