Section 6.1, Problem 34 

This page explains some Maple commands that you may find helpful for problems such as #34 from section 6.1. 

Tip: To get help about any command, type a question mark followed by the command name and press enter.  For example, to get help about the solve command, type ?solve[ENTER] 

Problem 34 asks us to find the point of intersection of two curvs, which amounts to solving Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi( for x.  We could use the solve command, but then we get a messy expression with lots of fractions and roots, as shown below. 

Typesetting:-mrow(Typesetting:-mi( 

0, `+`(`*`(`/`(1, 6), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(2, 3)), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `-`(`/`(1, 3))), `+`(`-`(`...
0, `+`(`*`(`/`(1, 6), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(2, 3)), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `-`(`/`(1, 3))), `+`(`-`(`...
0, `+`(`*`(`/`(1, 6), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(2, 3)), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `-`(`/`(1, 3))), `+`(`-`(`...
0, `+`(`*`(`/`(1, 6), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(2, 3)), `*`(`^`(`+`(316, `*`(36, `*`(`^`(77, `/`(1, 2))))), `/`(1, 3)))), `-`(`/`(1, 3))), `+`(`-`(`...
(1)
 

Instead, we should use the fsolve command, which will give us a decimal number.  (The f stands for floating-point, which is another term for a decimal number.)  The syntax is fsolve( equation , variable ). 

Typesetting:-mrow(Typesetting:-mi( 

0., 1.174559410 (2)
 

We can also use the plot command to graph the equations.  The syntax is Typesetting:-mrow(Typesetting:-mi( where Typesetting:-mrow(Typesetting:-msub(Typesetting:-mi( and Typesetting:-mrow(Typesetting:-msub(Typesetting:-mi( are the equations we want to graph, and a and b are the lower and upper bounds of the plot window.  See the example below. 

Typesetting:-mrow(Typesetting:-mi( 

Plot_2d
 

We can even ask Maple to evaluate the integral for us.  The syntax is integrate( equation, x=a..b) where again a and b are the bounds of integration.  See the example below. 

Typesetting:-mrow(Typesetting:-mi( 

1.146467426 (3)