College of Engineering and Computer Science Mechanical Engineering Department Notes on Engineering Analysis February 1 2009 Larry Caretto Notes on Symbolic Integration in Matlab Definite integrals can be evaluated using the symbolic mathematics toolbox of Matlab This program can provide an algebraic result as well as a numerical value of the result The required commands and results are shown below Commands entered by the user follow the prompt The remaining text is program output The initial command syms x defines x as a symbolic variable If you do not use this command the variable is only treated as a typical variable in a computer program that represents a number With the syms command you can have the computer do symbolic algebra and calculus for you The next command in the list below format long e sets the appearance of the output to use a large number of significant figures and to be printed in a scientific format b The remaining commands which are used to find the integral f x dx have the form a int f x a b where f x is a Matlab string expression for the integrand and a and b are the lower and upper limits respectively The symbolic expression in the answer ans is then evaluated by the command double ans For example the first application of the int function calls for the integration of cos x 2 between x 1 and x 1 1 Note that Matlab defines the character pair pi to refer to It is not necessary to define this as a symbol The result of this command is shown as 4 pi If the upper and lower limits were not provided the answer would be shown as 2 pi sin pi x 2 The default variable used to store the result of Matlab commands is ans short for answer If is possible to assign the result to another variable by using a command of the form y int cos pi x 2 1 1 In this example the answer would start with y instead of ans Of course you would first have to use the syms y command to define y as a symbolic variable The remaining Matlab commands show below are the commands used to integrate cos x 2 times even powers of x from the limits of 1 to 1 Once a symbolic result is found the command double ans is used to print the numerical value A command not shown here pretty ans can be used to improve the appearance of symbolic results syms x format long e int cos pi x 2 1 1 ans 4 pi double ans 1 Matlab typically uses a apostrophe to signify the start and end of string variables However for the int command you can enter the string with or without the apostrophes The commands shown here do not use them However the first integration command could be written as int cos pi x 2 1 1 or int cos pi x 2 1 1 Jacaranda Engineering Room 3333 E mail lcaretto csun Mail Code 8348 Phone 818 677 6448 Fax 818 677 7062 ans 1 273239544735163e 000 int x 2 cos pi x 2 1 1 ans 4 pi 2 8 pi 3 double ans ans 2 411904428727790e 001 int x 4 cos pi x 2 1 1 ans 4 pi 4 384 48 pi 2 pi 5 double ans ans 1 002298892908609e 001 int x 6 cos pi x 2 1 1 ans 4 pi 6 5760 pi 2 120 pi 4 46080 pi 7 double ans ans 5 459022242030317e 002 Jacaranda Engineering Room 3333 E mail lcaretto csun Mail Code 8348 Phone 818 677 6448 Fax 818 677 7062