Math

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.

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

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1420 Austin Bluffs Pkwy, Colorado Springs, CO USA 80918

719-255-8227 (UCCS), 800-990-8227