find area integration

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November 11th 2008, 01:38 AM
jvignacio

find area integration

find the area between the graph of $y= 6x^2 - 42x + 60$ and the x-axis, between x=1 and x=4.

any ideas? thank you
November 11th 2008, 01:45 AM
mr fantastic

Quote:

Originally Posted by jvignacio

find the area between the graph of $y= 6x^2 - 42x + 60$ and the x-axis, between x=1 and x=4.

any ideas? thank you

Draw a graph and it should be clear that you need to consider two seperate integrals:

1. $\int_1^2 6x^2 - 42x + 60 \, dx$ .

2. $\left| \int_2^4 6x^2 - 42x + 60 \, dx \right|$ .
November 11th 2008, 03:36 AM
jvignacio

Quote:

Originally Posted by mr fantastic

Draw a graph and it should be clear that you need to consider two seperate integrals:

1. $\int_1^2 6x^2 - 42x + 60 \, dx$ .

2. $\left| \int_2^4 6x^2 - 42x + 60 \, dx \right|$ .

for the graph should i just plug in some values for x then get points for y? being an absolute intergration does it make a difference?
November 11th 2008, 03:40 AM
mr fantastic

Quote:

Originally Posted by jvignacio

for the graph should i just plug in some values for x then get points for y? being an absolute integer does it make a difference?

If you're studying integral calculus you should know how to draw the graph of a parabola. Especially one whose equation factorises so easily.

I don't know what you mean by absolute integer?
http://www.mathhelpforum.com/math-he...60062b2b-1.gif means take the magnitude of the integral (since the integral itself is negative).
November 12th 2008, 04:59 AM
jvignacio

Quote:

Originally Posted by mr fantastic

If you're studying integral calculus you should know how to draw the graph of a parabola. Especially one whose equation factorises so easily.

I don't know what you mean by absolute integer?
http://www.mathhelpforum.com/math-he...60062b2b-1.gif means take the magnitude of the integral (since the integral itself is negative).

$\int_1^2 6x^2 - 42x + 60 dx$ + $\int_2^4 6x^2 - 42x + 60 dx$

i got -9 for my final answer?
November 12th 2008, 11:48 AM
mr fantastic

Quote:

Originally Posted by jvignacio

$\int_1^2 6x^2 - 42x + 60 dx$ + $\int_2^4 6x^2 - 42x + 60 dx$

i got -9 for my final answer?

How can an area between the curve and the x-axis be negative?

The answer has to be positive. Did you draw the graph?

It looks like you haven't taken the magnitude of $\int_2^4 6x^2 - 42x + 60 \, dx$ like I said to. But without seeing th details of your calculation it's impossible to know for sure what mistakes you have made.
November 12th 2008, 12:32 PM
jvignacio

Quote:

Originally Posted by mr fantastic

How can an area between the curve and the x-axis be negative?

The answer has to be positive. Did you draw the graph?

It looks like you haven't taken the magnitude of $\int_2^4 6x^2 - 42x + 60 \, dx$ like I said to. But without seeing th details of your calculation it's impossible to know for sure what mistakes you have made.

when i integrated $\int_2^4 6x^2 - 42x + 60 \, dx$ that gave me a -20.. so hence my result being a negative but when u say magnitude, what do this mean?

do i need to change the all the signs to its opposite .. - = + and + = - ?

that gives me 31
November 12th 2008, 01:13 PM
mr fantastic

Quote:

Originally Posted by jvignacio

when i integrated $\int_2^4 6x^2 - 42x + 60 \, dx$ that gave me a -20.. so hence my result being a negative but when u say magnitude, what do this mean?

do i need to change the all the signs to its opposite .. - = + and + = - ?

that gives me 31

The magnitude of -20 is 20.

So yes, 31 is the answer.