Approximate the value of the integral of 6/(1+2x) with respect to x from 0 to 2. Use 4 subintervals of equal width and use the left endpoints.
delta x = (b-a)/N
The Attempt at a Solution
The integral is the sum of 6/(1+i) from i = 0 to i = N-1 or 3 all multiplied by delta x, or 1/2.
(1/2)(6 + 3 + 2 + (6/4))
= 3 + 3/2 + 1 + 3/4 = 4 + 1.5 + 0.75 = 5.5 + 0.75 = 6.25 = 25/4.
1) This is correct without the N term in the sum, right? I'm wondering because usually I have to take the limit as N approaches infinity but the N doesn't exist here, since N has already been defined.
2) Also is my work correct in general? I'm still getting a hang of this Reimann sum notation with the indices and n subintervals and the x star notation. I'll have to learn Latex another day!