MATH/CMSC 206 - Introduction to Matlab

Answers to Self-Test

1. Try using int to symbolically calculate the definite integral of the function f(x) = sqrt(x + ln(x)) over the interval [10, 20]. It may take a while. After all that waiting, when you finally see the answer you will be very disappointed! That was useless. Now try it using quad.

syms x
int(sqrt(x + log(x)), 10, 20)

Warning: Explicit integral could not be found. 
 
ans =
 
int((x + log(x))^(1/2), x = 10..20)

quad(@(x) sqrt(x + log(x)), 10, 20)

ans =

   41.8953

2. Try to find the definite integral of the function f(x) = 2^sin(x) over the interval [1, 2] using both symbolic and numerical methods. Hint: To get this function to work properly with quad, you'll have to use the symbol .^ instead of ^ for exponentiation. Later, you'll learn why!

int (2^sin(x), 1, 2)

Warning: Explicit integral could not be found. 
 
ans =
 
int(2^sin(x), x = 1..2)

quad(@(x) 2.^sin(x), 1, 2)

ans =

    1.9413