How to Calculate the Area of a Square Using Definite Integrals?

[merven]

THE AREA OF A SQUARE WITH SIDE LENGTHS EQUAL TO THE DEFINITE INTEGRAL OF (0.43890022*X) FROM 1 TO 10


please help me...

Merven

 

[siddharth]

You need to show your work before you get help. What have you done with this question?

 

[merven]

ok well i posted it in the calculus forums but no one helped...
my friend is making a new website and he told me the only way i could get a peak is by solving this equation, and the reason he did this is becasue he knows far to well i can't do math, I recenty graduated HS and know nothing of calculus, that's why I am askign here, if someone would be willing to help me or to even give me crash corse because they don't think its right to just give me the answer i would be more then willing to try and learn...
thanks
Merven

 

[steven10137]

lol; most odd thing i have ever heard ...
but, if your story is true, i shall try and help.

I take it you would know that a square has equal length sides?
hence the area of the square is equal to the length by width (or in this case $$l^2$$:
$$A(square) = l^2$$
(if u really need: http://en.wikipedia.org/wiki/Square_(geometry))

In regard to the next section, i doubt it will be even the slightest bit understandable, but none-the-less ...
A definite integral basically finds the area underneath a graph in a set region i.e. between a and b: http://en.wikipedia.org/wiki/Image:Integral_as_region_under_curve.svg
where f(x) is your function, such that: $$f(x) = 0.43890022x$$
but for our purposes, we just want to find the numerical answer for this integral as a means of determining the area of the square.

The definite integral notation for this is:
$$\int_{1}^{10} {0.43890022x}$$
This ican be explained as; the definite integral between 1 and 10 for the equation 0.43890022 as required.

Now we can simplify this integral and obtain a numerical answer:
$$\int_{1}^{10} {0.43890022x}$$
$$= 0.43890022 \int_{1}^{10} {x}$$ (taken out factor)
$$= 0.43890022(\frac {x^2}{2})$$ between 1 and 10
$$= 0.43890022 ((\frac {10^2}{2}) - (\frac {1^2}{2}))$$
plug that into your calculator and you get:
$$21.72556089$$

remember from before:
$$A(square) = l^2$$
therefore:
$$A(square) = 21.72556089^2$$
$$=471.999996$$

wow that took longer than I thought, but yeh, hope this helps your cause.
You must understand that you cannot learn how to do definite integration with no understanding of basic calculus methods etc; for the parts you don't understand, just take them as facts ...
Steven

 

[arunbg]

Assuming of course that the variable of integration is X and that X varies from 1 to 10 ...

 

[steven10137]

hehe, yer ...

in respect to the problem given; could it be anything else??
or is that just complicating things more?
lol

Steven

 

[arunbg]

lol, nah it had to be X, I was just pointing out ways for the OP to get back at his supercilious friend

 

[steven10137]

haha, yeh good point and idea ...
pretty nasty form of entrance don't you think?

 

[matt grime]

As long as you know what 'integral means' calculus is completely irrelevant to the question. It's just a straight line graph - you can find the area by elementary means.

 

[merven]

omg if that trully is the answer, i got it right when i used one fo the calculators. but double guessed and threw it out since i had no clue. lol wow steven10137 you are my hero... lol now i have to see what he says, ill come back and post his reply :) thanks a million guys
Merven

 

[steven10137]

omg if that trully is the answer, i got it right when i used one fo the calculators. but double guessed and threw it out since i had no clue. lol wow steven10137 you are my hero... lol now i have to see what he says, ill come back and post his reply :) thanks a million guys
Merven

not at all
:)

 

[merven]

lol its awsome ty again, he was shocked but gave in after i got angry LOL, thank you all again