Use finite approximation to estimate the area under the graph...

[MajinBrian]

Use finite approximation to estimate the area under the graph of f (x) = 4x² and above the graph of f (x) = 0 from x₀ = 0 to x_n = 14, using
i) a lower sum with two rectangles of equal width.
ii) a lower sum with four rectangles of equal width.
iii) an upper sum with two rectangles of equal width.
iv) an upper sum with four rectangles of equal width.
Simplify your answer.

 

[stapel]

Use finite approximation to estimate the area under the graph of f (x) = 4x² and above the graph of f (x) = 0 from x₀ = 0 to x_n = 14, using
i) a lower sum with two rectangles of equal width.
ii) a lower sum with four rectangles of equal width.
iii) an upper sum with two rectangles of equal width.
iv) an upper sum with four rectangles of equal width.

What is the width of the interval over which you're to find the area?

If this width is split into two sub-intervals with equal widths, how wide are those sub-intervals?

Then what must be the sub-interval endpoints?

If you're doing a lower sum then, looking at the graph, which endpoint from each sub-interval should you use?

What values then do you get?

Follow the same reasoning for four rectangles, and then for the upper sums. If you get stuck, please reply showing all of your work and reasoning so far. Thank you!