(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need to use the right endpoint formula to find the area under the curve f(x) = 4-x^{2}over the interval [1,2]

I integrated this problem and got 5/3. But doing it the long way got me 11/3. Can someone where I made my mistake on applying the right endpoint formula, thanks!

2. Relevant equations

right endpoint formula = [tex] f(\frac{b-a}{n}*k) [/tex] and [tex]

\sum_{k=1}^n K^2 = \frac{n(n+1)(2n+1)}{6}[/tex]

3. The attempt at a solution

Before I use the right endpoint formula I tried integration and got:

[tex]\int_{1}^{2} 4-x^2 dx = \left[ 4x-\frac{x^3}{3}\right]_{1}^{2} = \frac{5}{3}[/tex]

here is what I got using the right endpoint formula:

[tex] \lim_{n\rightarrow\infty} \sum_{k=1}^n f(\frac{k}{n})*\frac{1}{n}

= \left[4-(\frac{k^2}{n^2})\right]*\frac{1}{n} [/tex]

[tex] = \frac{4}{n} - \frac{K^2}{n^3} [/tex]

[tex] \lim_{n\rightarrow\infty} 4 - \frac{1}{n^3}(\frac{(n(n+1)(2n+1)}{6} )[/tex]

[tex] = 4 - \frac{1}{3} = \frac{11}{3} [/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help me check my HW (area under a curve)

**Physics Forums | Science Articles, Homework Help, Discussion**