Question

Which of the following is a right-hand endpoint Riemann sum approximation to integral f(x)dx from 1 to 4 with six equal subdivisions?

Answer 1

a. f(1)+f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)
b. f(1.5)+f(2)+(2.5)+f(3)+f(3.5)+f(4)
c. 1/4[f(1)+f(1.5)+f(2)+f(2.5)+f(3)+(3.5)]
d. 1/2[f(1)+f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)
e. 1/2 f(1.5)+1/2f(2) + 1/2f(2.5) + 1/2f(3) + 1/2f(3.5) + 1/2f(4)

Answer 2

@myininaya

Answer 3

So our interval is,
\[\Large\rm (1,4)\]So let's find the width of each rectangle ( delta x ).
We'll split the interval into 6 equal pieces.\[\Large\rm \Delta x=\frac{4-1}{6}\]

Answer 4

So that's the width of each rectangle. 1/2 right?

Answer 5

4-1/6 = 1/2, so yea

Answer 6

Would it be d?

Answer 7

Yes very good!
Since we're using `right endpoints`, the height of our `first` rectangle is f(1.5)