### Home > PC > Chapter 2 > Lesson 2.3.7 > Problem 2-158

The area under the function

*f*(*x*) = 3*x*^{3}+ 1 on the interval from 1 to 3 is to be approximated using 10 left-endpoint rectangles. Homework Help ✎Write the summation notation that will represent the area.

Make a small change to your answer in part (a) so that the sum will find the area using right-endpoint rectangles.

Make a small change to your answer in part (a) so that the sum will find the area using midpoint rectangles.

Sketch the function.

Draw 10 rectangles between *x* = 1 and 3.

What is the width for each rectangle? What are the *x*-values for the heights?

What expression needs to go into *f*(*x*) to convert the integer values to 1, 1.2, 1.4, 1.6..., 2.8?

Write the summation now. Be careful with your *k*-values.

*x*_{0} = 1; *x*_{1} = 1.2; *x*_{2} = 1.4; *x*_{3} = 1.6; ...; *x*_{9} = 2.8

0.2*k* + 1

What *k*-values should you start and stop with?

Change the inside function to: 0.2*k* + 1.1 so that it is starting at the middle of each rectangle.