${{I}_{2}}=\int\limits_{1}^{4}{\left( 2x+4\sqrt{x} \right)dx}$
${{I}_{2}}=\int\limits_{1}^{4}{2x+4.{{x}^{\dfrac{1}{2}}}}$
${{I}_{2}}=2.\dfrac{{{x}^{2}}}{2}+4.\dfrac{{{x}^{\dfrac{3}{2}}}}{\dfrac{3}{2}}\,\,\,\,\,\mathop{\left. {} \right|}_{1}^{4}$
${{I}_{2}}={{x}^{2}}+\dfrac{8{{x}^{\dfrac{3}{2}}}}{3}\,\,\,\,\,\mathop{\left. {} \right|}_{1}^{4}$
${{I}_{2}}={{x}^{2}}+\dfrac{8}{3}\sqrt{{{x}^{3}}}\,\,\,\,\,\mathop{\left. {} \right|}_{1}^{4}$
${{I}_{2}}=\left( {{4}^{2}}+\dfrac{8}{3}\sqrt{{{4}^{3}}} \right)-\left( {{1}^{2}}+\dfrac{8}{3}\sqrt{{{1}^{3}}} \right)$
${{I}_{2}}=\dfrac{101}{3}$
……………………………………………
${{I}_{3}}=\int\limits_{0}^{1}{\left( 3{{x}^{4}}-4{{x}^{2}} \right)}dx$
${{I}_{3}}=3.\dfrac{{{x}^{5}}}{5}-4.\dfrac{{{x}^{3}}}{3}\,\,\,\,\,\mathop{\left. {} \right|}_{0}^{1}$
${{I}_{3}}=\dfrac{3}{5}{{x}^{5}}-\dfrac{4}{3}{{x}^{3}}\,\,\,\,\,\mathop{\left. {} \right|}_{0}^{1}$
${{I}_{3}}=\left( \dfrac{3}{5}{{.1}^{5}}-\dfrac{4}{3}{{.1}^{3}} \right)-\left( \dfrac{3}{5}{{.0}^{5}}-\dfrac{4}{3}{{.0}^{3}} \right)$
${{I}_{3}}=-\dfrac{11}{15}$
