What is the Riemann Sum Approximation for this Homework Problem?

[Qube]

Homework Statement

https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1456973_10201043975243279_1765184125_n.jpg?oh=05b39611ad70d28d837ed219e1b0f2aa&oe=52838593

Homework Equations

The area can be approximated by using the sum of the areas of the rectangles. Area of rectangle = change in x * y (given by f(x)).

The Attempt at a Solution

I've taken calculus I, II, and diff eqs., but I haven't done this for a while. I'm doing it mostly from intuition and memory.

My x-values are 0, 0.5, 1, and 1.5. This gives me the x-values for a left-handed approximation since I'm not going up to 2.

My y-values are therefore 6, 3, 2, and 3/2.

0.5(6) + 0.5(3) + 0.5(2) + 0.5(3/2) = 3 + 3/2 + 1 + 3/4 = 25/4.

 

[Mark44]

Homework Statement

https://scontent-b-mia.xx.fbcdn.net/hphotos-prn2/v/1456973_10201043975243279_1765184125_n.jpg?oh=05b39611ad70d28d837ed219e1b0f2aa&oe=52838593

Homework Equations

The area can be approximated by using the sum of the areas of the rectangles. Area of rectangle = change in x * y (given by f(x)).

The Attempt at a Solution

I've taken calculus I, II, and diff eqs., but I haven't done this for a while. I'm doing it mostly from intuition and memory.

My x-values are 0, 0.5, 1, and 1.5. This gives me the x-values for a left-handed approximation since I'm not going up to 2.

My y-values are therefore 6, 3, 2, and 3/2.

0.5(6) + 0.5(3) + 0.5(2) + 0.5(3/2) = 3 + 3/2 + 1 + 3/4 = 25/4.

That is correct.