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Home > PCT > Chapter Ch2 > Lesson 2.3.7 > Problem 2-158

2-158.

The area under the function on the interval from to is to be approximated using left-endpoint rectangles. 

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

    Sketch the function.

    Draw rectangles between and .

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

    ; ; ; ; ;

    What expression needs to go into to convert the integer values to , , , , , ?

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

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

    What -values should you start and stop with?

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

    Change the inside function to: so that it is starting at the middle of each rectangle.