| 1. | The 6th LiveMath document (IT4AMIntegArea6.thp) shows the same speed-time graph of the car but it uses a calculus method, namely integration, to find the area under the curve. "Integ" is the value of the definite integral of y from x = a to x = b. |
| Question 17: | Compare the value of Integ with the limit in Q15 or the
value of TrapSum when n = 100. What do you observe?
|
| Question 18: | Hence explain the significance of the definite
integral of y from x = a to x = b.
|
| 2. | The equation of the curve is given as a function f(x)
= x2 where x is called a wildcard variable in
LiveMath. To enter x, type ?x.
You can change the equation of the curve and the limits of integration,
a and b, to find the area under the curve from x = a to x = b. Try the
following and record your answers in the Worksheet.
(a) f(x) = x3 for x = 1 to 2, [highlight RHS of f(x) and type ?x^3 to get x3] (b) f(x) = 5sin(x) for x = 0 to  /2,
[use Ctrl Alt P to type ;click
on graph to refresh]
(c) f(x) = x2 for x = –1 to 1, (d) f(x) = x3 for x = –1 to 1, (e) f(x) = x3 for x = –1 to 0. |