Week 6: Integration and Applications

Question 1

What is the Riemann sum?

Answer 1

Riemann Sum is an approximate, integration method that uses rectangles of equal size to calculate area under the curve.

Question 2

Can you have a negative result from a Riemann Sum?

Answer 2

Yes. You can have a negative result from a Riemann Sum.

This is because the Riemann sum accounts for the “negative” area created by functions.

Question 3

What is the sum of power series for a power of 1?

Answer 3

1+2+3+⋯+n=(n/2)(n+1)

Question 4

What is the sum of power series for a power of 2?

Answer 4

1^2+2^2+3^2+⋯+n=(n/6 )(n+1)(2n+1)

Question 5

What is the sum of power series for a power of 3?

Answer 5

1^3+2^3+3^3+⋯+n=[(n^2)/6][(n+1)^2]

Question 6

How is the width of of the rectangles of the rectangles used in a Riemann Sum determined?

Answer 6

Δx = (b-a)/n