Exs. $1-28,$ use Wallis' formula.

$1.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}xdx.$

Ans. $\frac{}{4}.$

$2.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{2}xdx.$

$3.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{5}ydy.$

Ans. $\frac{8}{15}.$

$4.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}ydy.$

$5.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{4}d.$

Ans. $\frac{3}{16}.$

$6.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{8}d.$

$7.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{4}co{s}^{3}d.$

Ans. $\frac{2}{85}.$

$8.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}co{s}^{6}d.$

$9.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}co{s}^{2}d.$

$10.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{4}xco{s}^{5}xdx.$

$11.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{3}xco{s}^{3}xdx.$

$12.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{4}xco{s}^{4}xdx.$

$13.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{6}si{n}^{7}d.$

$14.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}co{s}^{5}si{n}^{5}d.$

$15.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{3}xco{s}^{6}xdx.$

$16.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{2}xco{s}^{4}xdx.$

$17.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{6}yco{s}^{6}ydy.$

$18.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}si{n}^{4}yco{s}^{7}ydy.$

$19.{\displaystyle \underset{0}{\overset{1}{}}}(1-x^2{)}^{\frac{1}{2}}dx.$ Put $x=sin.$

$20.{\displaystyle \underset{0}{\overset{a}{}}}{x}^2(a^2-x^2)dx.$ Put $x=$asin$.$