### Home > PC3 > Chapter 5 > Lesson 5.2.1 > Problem5-50

5-50.

The area under the curve $f(x)=3x^3+1$ on the interval from $x=1$ to $x=3$ is to be approximated using ten left endpoint rectangles.

1. Write the sigma notation that will represent the area.

Accurately sketch the function for $x=1$ to $x=3$.

Draw $10$ rectangles between $x=1$ and $3$. What is the width of each rectangle?

What are the $x$-values for the endpoints of the rectangles?

Write a linear expression for the endpoints: $1,1.2,1.4,1.6,...$

Substitute the linear expression you wrote in step 4 into the function for $x$. This will be the argument of your summation notation.

2. Modify your answer in part (a) to calculate the area using right endpoint rectangles.

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