1
Distances (again)
t(s) 0 v 30 Give two different estimates. 12 28 24 25 36 22 48 24 60 27
Example 1.1. Speedometer readings for a motorcycle at 12 second intervals are given:
2
Definite Integral
Recall what we just did. Definition 1. If f is a
1
Volumes
Finding volumes is very similar to finding areas. With areas, we approximated the region by shapes we did know and then made the approximation better. With volumes for regions we don't know, we do the same thing. To start, the area of gen
Calculus II - MAT 142
Summer II, 2006 TR 6:00pm - 9:00pm
"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gor
1
Work
Another use of calculus is to calculate the amount of work done completing a task. For basic things, we have the formula Work = Force Distance Example 1.1. Do an example in metric and Imperial. But just like with our formulas for velocity a
1
Indefinite Integrals
The fundamental theorem of calculus shows just how important antiderivatives are. Since we'll be using them so frequently from now on, we introduce a notation for them. Actually, the FTC gives us an intuitive notation for the
Homework # 1 Due: 7/18/06 1. Use the sum definition of an integral to evaluate
4 2 (x 0
+ 2x - 3)dx
2. Use part 1 of the fundamental theorem of calculus to find the derivatives of the following functions: 1 dt 2 -3 t + t 1 3 (b) g(x) = cos d (a) g
Homework # 2 Due: 7/25/06 1. Find the are bounded by the given curves. (a) y = sin x, y = x, x = 0, x = /2 (b) y = x, y = 3 x (c) y = 3 - x2 ,y = x2 + 1,x = -2,x = 2 2. Find the volume obtained by rotating the region bounded by y = 5 - x2 ,y = 1 abo
1
Review
Limit laws Derivative rules
2
Antiderivatives
Recall when we were looking at the motion of a particle, we were given a function for its position at a given time. We could figure out how fast it was moving by looking at the derivative.