Math 1350 - Integrals

 

MAPLE is a powerful tool in finding integrals. The MAPLE command to integrate is int.

 

Example 1:

 

integrate f(x) = 2*x^3.

 

> f:=x->2*x^3;

> int(f(x), x);

Warning: MAPLE forgets to put the constant C.

 

Example 2:

 

integrate f(x) = 2*x^3 from x=0 to x=2. Plot f(x) and its integral on the same graph.

> int(f(x), x=0..2);

Name the integral int_f. Use the MAPLE command unapply to make int_f a function of x for MAPLE.

> int_f:=unapply(int(f(x), x), x);

 

> plot([f(x), int_f(x)], x=0..2);

Can you say what curve on the graph belongs to what function?

 

Exercises:

 

integrate the following function. Plot the function and its integral on the same graph.

  1. f(x) = e^x from x = 0 to x = 4. Use the MAPLE command evalf(%) to get the answer as a number.
  2. f(x) = sin(x) from x = p/2 to x = -p.
  3. f(x) = tan(x) from x = p/2 to x = -p.
  4. f(x) = tan(x/2) from x = p/2 to x = -p.
  5. f(x) = tan(x)/2 from x = p/2 to x = -p.