Estimate the area under the graph of f ( x ) = 1 /(x + 3) over the interval [ 1 , 4 ] using five approximating rectangles and right endpoints. Do the same for the left end points .

Answer 1

The width of the rectangles is (4-1)/5 = .6 . The x values will be (1, 1.6, 2.2, 2.8, 3.4 and 4)

To find the area you need only add up the areas of the rectangles which are .6*f(x_L) or .6*f(x_R) corresponding to the left and the right side of the rectangle:

The left side approximation is .6( f(1)+f(1.6)+f(2.2)+f(2.8)+f(3.4)) where f is the function evaluated at those points.

I'll leave the right- side approximation to you.