Question

Find the area of the region of the graph... f(x)=-1/3x+4
a=12
b=0

Answer 1

Where's the graph?

Answer 2

I think they are trying to integrate f(x) from x = 0 to x = 12.

Answer 3

Just integrate from 0 to 12
\[ \int\limits_{0}^{12}-1/(3x+4)dx\]

Answer 4

That's the more advanced method thingy that I am supposed to learn next year. I've learned
\[\sum_{i=1}^{n}f(a+(b-a)i/n)((b-a)/n)\]
but I don't understand how I'm supposed to use it, if that makes sense

Answer 5

I have \[\sum_{i=1}^{50}\left[ -1/3\left( 12i/n \right) +4\right]\left( 12/n \right)\]

Answer 6

Livey, do you know how to use geogebra? That would make visualizing this WORLDS easier. :)

Answer 7

geogebra?

Answer 8

http://www.geogebra.org greatest FREE software out there for dynamically visualizing mathematics. :D

Answer 9

could you just tell me how to solve the rest of the problem? It's kind of urgent and I don't want to download anything.

Answer 10

Basically what you're doing is finding the area under the curve by counting up the area of little rectangles. You find the area of these rectangles by taking the interval from a to b, splitting it up into n parts

(b-a) / n (that's the width)

and multiplying by the function evaluated at each of the n sub-parts of the interval.

That's the f(a + (b-a)i/n) part where i gives you 1/n, 2/n, 3/n... until you get n/n which is just 1 and leaves you with f(b).

Answer 11

@LivyLou Why do you use sigma from 1 to 50?

Answer 12

It's called a riemann sum.

http://www.math.hmc.edu/calculus/tutorials/riemann_sums/

Geogebra does this in about 2 seconds. :-p

Answer 13

It's part of the problem. I guess I forgot to mention it earlier, but it says "area of the region in the graph using n rectangles of equal width" and n for this problem is 50

Answer 14

If so, the width = ( b-a) /n = 12/50

Answer 15

@mathteacher1729 My calculator has a program to do the exact same thing, but I need to know how to solve it by writing out the process

Answer 16

FOR n = 50 ???

Answer 17

That is an ABSURD amount of computation.

Answer 18

(to do by hand)

Answer 19

@LivyLou are you sure?

Answer 20

the 50 on top of sigma may not be right, I'm not good at this, but the question does that to use 50 rectangles to find the approximate area

Answer 21

Do you have the answer?