\[\LARGE {\color {red}{Questions\ from\ Unit-III\ and\ Unit-IV}}\]
\[Date:\ 10-05-2022\ \hspace{10cm}\ Max\ Marks:\ 4\ ×\ 5\ =\ 20m\]
\[1.\ Evaluate:\ (i)\ \int (\sqrt{x}\ +\ \frac{1}{\sqrt{x}}) \ dx\ \hspace{2cm}\ (ii)\ \int cos\ x\ cos\ 12\ x\ \ dx\ \hspace{8cm}\]
\[2.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ \frac{6x^2\ -\ 1}{ 2x^3\ -\ x\ +\ 5}\ dx\ \hspace{2cm}\ (ii)\ \int\frac{sin\ \sqrt{x}}{\sqrt{x}}\ dx\ \hspace{10cm}\]
\[3.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ x^3\ log\ x\ dx\ \hspace{2cm}\ (ii)\ \int x\ e^{-5x}\ dx\ \hspace{10cm}\]
\[4.\ Evaluate:\ \hspace{2cm}\ (i)\ \int\ x^2\ sin\ 4x\ dx\ \hspace{2cm}\ (ii)\ \int x^2\ e^{-7x}\ dx\ \hspace{10cm}\]
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