Unit 6 - Integration and Accumulation of Change

Question 1

Riemann Sums

Answer 1

The Left Hand Rule says to evaluate the function at the left-hand endpoint of the subinterval and make the rectangle that height. In , the rectangle labelled “LHR” is drawn on the interval [2,3] with a height determined by the Left Hand Rule, namely f(2)=4.

The Right Hand Rule says the opposite: In
, the rectangle labelled “RHR” is drawn on the interval [0,1] with a height determined by the Right Hand Rule, namely f(1)=3.

Then take the average of both

Question 2

How to find the area under a curve?

Answer 2

Find the definite integral

Question 2

Midpoint rule

Answer 2

The Midpoint Rule says that on each subinterval, evaluate the function at the midpoint and make the rectangle that height. In , the rectangle labelled “MPR” is drawn on the interval [1,2] with a height determined by the Midpoint Rule, namely f(1.5)=3.75.

Question 3

Summation of i^2

Answer 3

(n)(n+1)(2n+1)/6

Question 3

Summation of i^3

Answer 3

[(n^2)(n+1)^2]/4