Question

Use MATLAB to determine the following integrals. a) Determine cosh r dx. (See section 1.9.1 of the MATLAB Manua. (b) Determine2exp-6r) dr. Use the pretty command to make your answer more readable. (Use help pretty for more information.) Enter int (sqrt (log(x^2-1))), and explain the output. (c) d) Computer programs can do many calculations very quickly but can make mistakes. We must therefore check that they are working. Our knowledge of mathematics helps with this 10 Use MATLAB to determinesin(t) dt. Does this answer make sense? Why? (You might want -10 to think about properties of your graphs in questions 1.)

Answer 1

Matlab code for finding integral clear all close all &Question a. syms x fprintf('a. Integration of f(x)-cosh (x) is fl (x)-cosh (x) zz-int(f1 () disp (zz) Question b. £2 (x)-x^2+exp(-6*x) ; zz-int(f2 (x)); fprintf(a. Integration of f (x)x 2*exp(-6*x) is \n') pretty (22) %Question c. f3 (x) sqrt (log (x*2-1) zz=int ( f 3 ( x)); fprintf(c. Integration of f () sgrt (log (x 2-1) is \n) disp(zz) fprintf ( For this function analytic integration is not possible.In eQuestion d fun = @(t) t."2.*sin(t); val-integral (fun,-10,10)i fprint f ( \nIntegration of In',val) t."2.*sin (t) for limit [-10 10] is %f plotting the function tt-linspace (-10,10); vv=fun (tt): plot (tt, vv, 'linewidth',2) xlabel('t') ylabel('f(t)' title( 't vs. f (t) plot' fprintf( 'As it is odd function the integral value is o.1n') 용号号응용号号응용号号응용号号응용号号 End of Code 욤융응용욤융융욤욤융융욤욤융융욤욤융 a. Integration of f(x)-cosh(x) is sinh(x) a. Integration of f(x)-x*2 exp (-6*x) is exp -6 x) (36 x + 12 x + 2) 216 c. Integration of f(x)-sqrt (log(x*2-1)) is int (log(x*2 - 1) *(1/2), x)

For this function analytic integration is not possible Integration of t. "2.*sin(t) for limit /-10 101 is -0.000000. As it is odd function the integra value is o. t vs. D plot 80 60 40 20 -20 60 10 8 -2 468 10 Published with MATLABR R2018a

%%Matlab code for finding integral
clear all
close all

%Question a.
syms x
fprintf('a. Integration of f(x)=cosh(x) is ')
f1(x)=cosh(x);
zz=int(f1(x));
disp(zz)

%Question b.
f2(x)=x^2*exp(-6*x);
zz=int(f2(x));
fprintf('a. Integration of f(x)=x^2*exp(-6*x) is \n')
pretty(zz)

%Question c.
f3(x)=sqrt(log(x^2-1));
zz=int(f3(x));
fprintf('c. Integration of f(x)=sqrt(log(x^2-1)) is \n')
disp(zz)

fprintf('For this function analytic integration is not possible.\n')

%Question d.
fun = @(t) t.^2.*sin(t);
val=integral(fun,-10,10);
fprintf('\nIntegration of t.^2.*sin(t) for limit [-10 10] is %f.\n',val)

%plotting the function
tt=linspace(-10,10);
vv=fun(tt);
plot(tt,vv,'linewidth',2)
xlabel('t')
ylabel('f(t)')
title('t vs. f(t) plot')
fprintf('As it is odd function the integral value is 0.\n')

%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%