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QUESTION $4$

$[21]$

$4\mathrm{.}1$ Determine the following integrals:

$4\mathrm{.}1\mathrm{.}1{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(2-x{)}^{\frac{3}{2}}dx$

$4\mathrm{.}1\mathrm{.}2{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{xdx}{3x^2+2}$

$4\mathrm{.}1\mathrm{.}3{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{e}^{tan4x}se{c}^{2}4xdx$

$4\mathrm{.}1\mathrm{.}4{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{e^x-e^{-x}}{e^x+e^{-x}}dx$

$4\mathrm{.}2$ Find the area enclosed by the curves $y=2-x^2$ and $y=3x-2.$