The discussion focuses on approximating the area under the curve defined by the function f(x) = x² + x using the left endpoint method with four rectangles over the interval [0, 4]. Participants clarify that the area of each rectangle is calculated using the formula A = b * h, where b is the width and h is the height determined by the function value at the left endpoint. The calculated area using this method results in 88/3 or approximately 29.3333. The conversation also touches upon the right endpoint method, questioning whether the results would be the same.
PREREQUISITESStudents studying calculus, educators teaching Riemann sums, and anyone interested in numerical methods for approximating areas under curves.
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?