The problem involves approximating the area bounded by the curve f(x) = x² + x, the x-axis, and the line x = 4, using left and right endpoint rectangles. Participants are exploring the method of Riemann sums for this calculation.
The discussion is ongoing, with some participants sharing their calculations and questioning the differences in results when using left versus right endpoints. Guidance has been offered on the general approach to calculating areas using rectangles.
There are indications of confusion regarding the calculations and the relationship between left and right endpoint approximations. Some participants express uncertainty about the initial steps and the method of summing areas.
tjohn101 said:Homework Statement
Use the left endpoint graph with the given number of
rectangles to approximate the area bounded by the
curve f (x), the x-axis, and the line x = 4.
f(x)=x2+x
Homework Equations
No idea.The Attempt at a Solution
Once again, not a clue how to start this.
tjohn101 said:Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
What did you do to calculate this? I came up with a different answer.tjohn101 said:Okay, I kind of guessed my way through it based on my notes and came up with 88/3 or 29.3333_ . Now, the next question asks me to do the same thing, but use the right endpoint graph. Wouldn't the answers be the same?
Yep, that's really all there is to a problem of this type. You want to split up the interval, calculate the height at whichever point you're using (left, right, mid), calculate the area of each rectangle, and sum them up.tjohn101 said:So for the left endpoints I just do A=b*h and then add them all up?
Same for the right?