Question

Calculate the left Riemann sum for the given function over the interval [0, 10], using n = 5. (Give the answer to two decimal places.)


f(x)=16e^-x

I'm confused on how to approach these kind of problems. Can someone please help me solve this, and maybe find a shortcut method if there is one?

Answer 1

divvy your interval into 5 equal pieces, what is the length of each piece?

Answer 2

\[\sum_{i=0}^{n-1} f(a+i\frac{b-a}{n})\frac{b-a}{n}\]

Answer 3

Sorry for the delay, had some technical difficulties. I counted 2 as being the length of each piece

Answer 4

good, the b-a/n = 2, a=0, n=5

\[\sum_{i=0}^{4} 2f(2i)\]
\[\sum_{i=0}^{4} 2(16e^{-2i})\]
\[32\sum_{i=0}^{4} e^{-2i}\]
\[32(e^{-2.0}+e^{-2.1}+e^{-2.2}+e^{-2.3}+e^{-2.4})\]
\[32(1+e^{-2}+e^{-4}+e^{-6}+e^{-8})\]