Estimate the area under the graph of f(x) = 2x^3 + 3 from x= -1 to x=5, first using 6 approximating rectangle and right endpoints, and then improving your estimate using 12 approximating rectangles and right endpoints. When using the left and right endpoints, is there a different way to compute each?

Answer 1

You are being asked to perform a numerical integration. Add up the values of f(x) at x= 1,2,3,4,5 and 6 . Multiply the sum by the interval, 1.

Then do it again at x= 1/2, 1, 3/2, 2,. ...6, and multiply the sum by the interval, 0.5.

If you use the average of left and right endpoints, you will be using the trapezoidal rule. It should be more accurate approximation to the integreal