$A={\displaystyle \underset{0}{\overset{1}{}}}(1+\frac{sinx}{x+1})*dx$

Ue $n=7$

Ans $=1\mathrm{.}2826$

B$.$ Evalude the following Numerical integration by using. Simpson's Rule $q{q}^{****}$

${\displaystyle \underset{4}{\overset{8}{}}}\frac{1}{\sqrt[\phantom{2}]{16x-x^2}}dx$

us $n=6$

$A_n=0\mathrm{.}816$

${\displaystyle \underset{1}{\overset{3}{}}}{e}^{65x}\frac{x}{\sqrt[\phantom{2}]{x^2+2}}*dx$

Use $n=4$

$3.{\displaystyle \underset{0}{\overset{6}{}}}\frac{1}{x^2+sinx+1}dx$

Use

Ans $=1\mathrm{.}6068$

$4.{\displaystyle \underset{1}{\overset{3}{}}}sinh(e^{-x})*dx$

Use $n=6$

An $0\mathrm{.}823844$