Chapter 9-Integrals

Question 1

Sequence

Answer 1

Set of numbers

Question 2

Series

Answer 2

Set of numbers that become added.

Question 3

Riemann sum

Answer 3

Summation(f(x_k)(deltaxk)) from k=1 to n.

Where the function hits the rectangle tells you what values to plug into your function.

Question 4

Trapezoid rule

Answer 4

A type of riemann sum. Can find areas.

Question 5

What is the limit of the Riemann sum

Answer 5

The integral. It’s where the deltas=0

Question 6

Backward time property

Answer 6

Integral(a,b)f(t)do=-integral(b,a)f(t)dr

Question 7

Speed up and do it again

Answer 7

Constant in an integral can be pulled out.

Question 8

Additive property

Answer 8

Check the equation on the word. We can combine two integral. It’s like integral addition postulate similar to segment addition postulate.

Question 9

Average value theorem

Answer 9

If the function is continuous and we get a certain value for the average value that means at least one point on the graph we are going at that rate.

Question 10

Fundamental theorem of calculus

Answer 10

Integral(a,b)f(x)dx=F(b)-F(a)

Question 11

Sigma notation

Answer 11

Sum(n=1) to whatever number and then equals the formula for how each sequence changes.

Question 12

Zero Integral Property

Answer 12

An integral from a to a, or basically integrating over the same point. This will get you an answer of zero.