Question

f(x)= 8 - 0.5x^2 on the interval [-1,4]
What is the approximate area under the curve using a right sum with 10 rectangles?

I've figured out:
Change in x = 5/n
f(xi) = 8 - 0.5(-1 + (5/n)i)^2

It's sigma notation that messes me up, can anyone help me understand this please?

Answer 1

\[\frac{ 5 }{ n } \sum_{i=1}^{n} (equation) \]
\[\frac{ 5 }{ n } \sum_{i=1}^{n} (8-0.5(-1+\frac{ 5i }{ n })^2\]
\[\frac{ 5 }{ n } \sum_{i=1}^{n}[8-0.5(1+\frac{ 10i }{ n }+\frac{ 25i^2 }{ n^2 })]\]
\[\frac{ 5 }{ n } [8-0.5(n+\frac{ 10 }{ n } (\frac{ n(n+1) }{ 2 })+ \frac{ 25 }{ n^2 } (\frac{ n(n+1)(2n+1) }{ 6 })]\]
multiply each term by n then take \[\lim_{n \rightarrow \infty} \]
i dunno if that's how your teacher tells you to do it, but that's how my teacher told me how to do it.
hope it helps?

Answer 2

Thank you SO much!