### Home > CALC > Chapter 2 > Lesson 2.2.2 > Problem 2-69

Using sigma notation, write a Riemann sum to estimate the area under the function

*f*(*x*) =*x*cos*x*for −2 ≤*x*≤ 6 with eight left endpoint rectangles of equal width. Then use the summation feature of your graphing calculator to calculate the estimated area. Homework Help ✎

Since area of a rectangle = (base)(height), start by finding the base, or Δ*x* of each rectangle. Divide the interval by the number of rectangles:

Next, find the height of each rectangle. The height is determined by *f*(*a* +Δ*xi*), where *a* = starting value on the *x*-axis.

*f*((−2) + (1)*i*) = *f*(−2 + *i*)

Finally, use sigma notation to represent the sum of all eight rectangles. Since these are left-endpoint rectangles, the index will start at 0 and end at *n* − 1, where *n* = number of rectangles.

Use your calculator to evaluate this sum.