DEFINITE INTEGRALS (Excercise Problems)

\[\underline{PART\ -\ A}\]
\[1.\ Evaluate\ :\ \int_1^2 (x\ +\ x^2)\ dx\ \hspace{15cm}\]
\[2.\ Evaluate\ :\ \int_0^1 (3x^2\ -\ 2x\ +\ 7)\ dx\ \hspace{15cm}\]
\[3.\ Evaluate\ :\ \int_1^3 (4x\ -\ 5x^2)\ dx\ \hspace{15cm}\]
\[4.\ Evaluate: \int_0^\frac{\pi}{4} sec^2 x\ dx\ \hspace{15cm}\]
\[\underline{PART\ -\ B}\]
\[5.\ Evaluate\ :\ \int_1^2 (x^2\ +\ x\ +\ 1)\ dx\ \hspace{15cm}\]
\[6.\ Evaluate\ :\ \int_0^1 \frac{dx}{\sqrt{1 – x^2}}\ \hspace{15cm}\]
\[7.\ Evaluate\ :\ \int_0^\frac{\pi}{2} (2 + sin x)^2 cos x \ dx\ \hspace{15cm}\]
\[\underline{PART\ -\ C}\]
\[8.\ Evaluate: \int_0^\frac{\pi}{2} \frac{sin^2 x}{ 1- cos x} \ dx\ \hspace{15cm}\]
\[9.\ Evaluate: \int_0^\frac{\pi}{4} tan\ x\ sec^2\ x \ dx\ \hspace{15cm}\]
\[10.\ Evaluate:\ \hspace{2cm}\ (i)\ \int_0^1\ (2x\ +\ 3)^4\ dx\ \hspace{2cm}\ (ii)\ \int_0^\frac{\pi}{2} cos^2 x\ dx\ \hspace{10cm}\]
\[11.\ Evaluate: \int_0^\frac{\pi}{2} log(tan\ x)\ dx\ \hspace{15cm}\]