Finding exact area with the Definite Integral
Okay i was busy trying to figure these things out and then i got stuck.
Now using the Riemann notation to calculate the area under the graph we get the following:
(I calculated )
They use rectangles under the graph to approximate the area. (6 rectangles and the x-axis value ranges from 0 to 3.)
Then the book goes further and says:
For any number of rectangles under the graph(Still ranging from 0 to 3 on the x-axis):
At the end we arrive at the following:
Up to there i understand perfectly.
Then from that we get
Now i have no idea why Shouldn't it just equal ?
And now we arrive at integration(Still for the graph ):
And the second question: Do we always have to use a Riemann sum to arrive at this part: ? What, no shortcut? :D
And could a mod please delete this(Posted by accident): http://www.mathhelpforum.com/math-he...html#post85119