Math 126 Section 5.7

Lets do the examples from Section 5.7. On the top of page 411
We have the following example. Here is how we express the following
intergral, in the Maple language. The answer appears below our typed
expression.

> int(1/(3*x -2),x);

Example 5

We assign the result of our expression to a variable which we call r1
We do this so we can check our answer by differentiation.

> r1 := int(x*sqrt(x^2 + 2*x + 4),x);

Lets differentiate the above. The diff command is Maples way of differentiating.
We assign the result of the differentiation to the variable r2. Notice we get a
complicated answer. By using the command simplify , we get back our original expression.

> r2 := diff(r1,x);

> simplify(r2);

Example 6

> r1 := int(x*(x^2 + 5)^8,x);

> r2 := diff(r1,x);

We'd like this anwer to match our original expression. Let's try the factor command
this time. We get back our original expression.

> factor(r2);

Example 7

> r1 := int(sin(x)^5*cos(x)^2,x);

We take the derivative of the above. Notice that in this case, Maple is at a loss to
simplify this expression so that it looks like the original. Even when we try to simplify
or factor. Try it! This shows some of the limitations of Computer Algebra Systems.
They don't always know how to put the answer in the simplist and most elegant
form.

> r2 := diff(r1,x);

> r2 := simplify(r2);

> r2 := factor(r2);

Example 8

Find the antiderivative F of f such that F(0) = 0. Graph F (x), f(x), and f'(x).

> r2 := x + 60*sin(x)^4*cos(x)^5;
r1 := int(r1, x);
r3 := diff(r2, x);

> plot([r1,r2,r3], x = 0..5, y = -7 ..10);