As you should have experienced in your previous Maple assignment, Maple is an excellent solver of equations that you might find hard to solve without its help. Another task Maple can do quite well is integrate functions.
Functions of one variable. Lets take the function x^2. What is the integral of x^2 with respect to x? Maple can calculate it as well; ask it to calculate by
int(x^2,x);Maple gives you an antiderivative of x^2. Yours is probably more general. How? You can also get Maple to evaluate this integral at given bounds by the command
int(x^2,x=0..2);Maple can also evaluate the limits at variable bounds. Try
int(x^2,x=t+2..y^2);
Double and Triple Integrals. Of course, you can have Maple calculate multiple integrals. Consider the function exp(y^2) on the region between the lines x=y, x=1, and y=0. You can find the values of this integral by the command
int(int(exp(y^2),x=0..y,)y=0..1);
1. From Section 5.1, graph both parametrizations in question 3. Do they give you the same curve?
2. Find a parametrization for an ellipse (x/a)^2+(y/b)^2=1. Write an integral for the length of the ellipse. Can you get Maple to evaluate this integral? What happens if a=2 and b=3?
3. Have Maple calculate the integral in Section 5.2, question 10. Graph the cycloid and the function you are integrating.
4. Do 5.3, question 28 with Maple. If you don't have a visual picture of the volume you are integrating, use Maple to create one.
5. Consider the functions f(x)=x^4-9x^3-46x^2+324x+360 and g(x)=100x.
Find the area of the bounded regions between the curves as follows.
Be sure to document your work in Maple.
Use Maple to factor f to find where it is zero.
Use those zeros to find a good window to graph f and g.
Find where the regions bounded by the curves are.
Use Maple to find the points of intersection of f and g.
Find the area of each region.
Sum to get the total area.
6. Do Section 5.4, question 14 with Maple. Again, if you can't visualize the region you are integrating over, have Maple help you.