Given a table, find the integral from 4 to 20.

Question

I was given the table:
x: 4, 8, 12, 16, 20
f(x): 11, 26, 18, 3, 39

I drew the graph but I cant take the right or left hand some because each would be a mixture of an over and under estimate so I am a little confused on how to go about this.

It asks to take the integral ∫4 to 20 of f(x) dx when n=4.

I calculated change in x to be 4 based off of n, but I have no idea about what to do from here.

It says to find the lower estimate, and the upper estimate.

Answer 1

The integral is the area under the curve.  This integral will be an estimate rather than exact, since you have to defined function.

 

If we take the sum of the area of the 4 rectangles, we get our integral.

 

Integral = ∑(common difference in x)f(x)

 

Integral = 4(11 + 26 + 18 + 3 + 39)