Question

Help Summation Notation

Answer 1

The question is attached @RadEn

Answer 2

@science0229

Answer 3

Do you know what the definition of the definite integral is?

Answer 4

no

Answer 5

\[\int\limits_{a}^{b}=\lim_{n \rightarrow \infty}\sum_{i=1}^{n}f(x _{i})\Delta x\]

Answer 6

\[\Delta x=\frac{ b-a }{ n }\]

Answer 7

ok

Answer 8

Do you know why that formula works?

Answer 9

why

Answer 10

Integral is defined as adding infinitely small rectangles under a curve in specific interval.

Answer 11

oh ook

Answer 12

http://www.sitemaker.umich.edu/hammondc/files/riemann_sum.png

Answer 13

In the picture, if the base of each rectangle is infinitely close to zero, and all of the area are added up, then you end up with the area under curve.

Answer 14

oh ok

Answer 15

Now, for a function, y=f(x), in the interval [a,b], the bases of each rectangle can be written as \[\frac{ b-a }{ n } or \Delta x\]

Answer 16

ok so \[Deltax=\frac{ 3 }{ n }\]

Answer 17

Correct!

Answer 18

ok

Answer 19

Wait...

Answer 20

There is one more part to this, and I almost missed it.

Answer 21

ok

Answer 22

\[x _{i}=a+(\frac{ b-a }{ n })i\]

Answer 23

Because

Answer 24

(b-a)/n is the LENGTH of the base of a rectangle, not the actual x-coordinate

Answer 25

I might've lost you there.

Answer 26

Sorry my internet disconnected