Integrate e^[x] between limit 0 to 3

Question

amistre64 · Answer

there are no bad spots to worry about; so what does e^x come from?  since it is a derivative of some function

amistre64 · Answer

$$f(x)=\int^{b}_{a} f'(x)\ dx=f(b)-f(a)$$

amistre64 · Answer

prolly some bad notation, but its off the cuff ;)

anonymous · Answer

this is int exp raise to power greatest integer x from 0 to 3

lalaly · Answer

do u know how to integrate e^x?

anonymous · Answer

this is only e^x .

amistre64 · Answer

if i read you right, yes

$$\int e^x = e^x$$

amistre64 · Answer

$$e^3-e^0=\ ?$$

amistre64 · Answer

greatest integer .... is that the ceiling function?

amistre64 · Answer

if so, we might have to do this in pieces

amistre64 · Answer

the wolf says greatest integer is the floor function ....

amistre64 · Answer

http://www.wolframalpha.com/input/?i=integrate+e%5E%28floor%28x%29%29+from+0+to+3

amistre64 · Answer

the area can be considered as adding up the area of the rectangular spaces beneath the graph.

using midpoints to make sure we are in each section gives me:

1*(e^[0.5]+e^[1.5]+e[2.5])

produces the same results

zarkon · Answer

$$\int_{0}^{3}e^{[x]}dx=\sum_{n=0}^{2}\int_{n}^{n+1}e^{[x]}dx$$
$$=\sum_{n=0}^{2}\int_{n}^{n+1}e^{n}dx=\sum_{n=0}^{2}e^{n}(n+1-n)dx=\sum_{n=0}^{2}e^{n}$$
$$=e^0+e^1+e^2$$