Area and Volume (Excercise Problems)

\[\underline{PART\ -\ A}\]
\[1.\ Find\ the\ Area\ bounded\ by\ the\ curve\ y\ =\ 2x^2\ \hspace{12cm}\]\[the\ X-axis\ and\ ordinates\ x\ =\ 0\ and\ x\ =\ 2\ \hspace{5cm}\]
\[2.\ Find\ the\ Area\ bounded\ by\ the\ curve\ y\ =\ \frac{1}{x}\ \hspace{12cm}\]\[the\ X-axis\ and\ ordinates\ x\ =\ 1\ and\ x\ =\ 2\ \hspace{5cm}\]
\[3.\ Write\ down\ the\ formula\ to\ find\ the\ Volume\ bounded\ by\ the\ curve\ y\ =\ f(x)\ \hspace{8cm}\]\[the\ X-axis\ and\ the\ lines\ x\ =\ a\ and\ x\ =\ b\ \hspace{7cm}\]
\[4.\ Find\ the\ Volume\ bounded\ by\ the\ curve\ y^2\ =\ 4\ a\ x\ \hspace{10cm}\]\[between\ x\ =\ 0\ and\ x\ =\ 2\ \hspace{5cm}\]
\[\underline{PART\ -\ B}\]
\[5.\ Find\ the\ Area\ bounded\ by\ the\ curve\ xy\ =\ 1\ \hspace{12cm}\]\[the\ X-axis\ and\ the\ lines\ x\ =\ 1\ and\ x\ =\ 2\ \hspace{5cm}\]
\[6.\ Find\ the\ Area\ bounded\ by\ the\ curve\ y\ =\ 4\ x\ -\ x^2\ \hspace{12cm}\]\[and\ the\ X-axis\ \hspace{5cm}\]
\[\underline{PART\ -\ C}\]
\[7.\ Find\ the\ Volume\ got\ by\ rotating\ the\ loop\ of\ \ y^2\ =\ 6\ +\ x\ -\ x^2\ \hspace{12cm}\]\[about\ the\ X-axis\ \hspace{5cm}\]

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