Math Is Fun Forum

Ansh Agrawal

Member

Registered: 2012-01-26

Posts: 11

Area using definite integrals ! please help !

PLEASE HELP ME ON THIS QUESTION. I have no idea what it means to ask and how to draw the curve mentioned in it. If anyone could throw some light on the concept behind this problem, especially the second part, it would be great.

Find the area A bounded by the X-axis, part of the curve y = 1 - (8/x^2) and the ordinate x = 4 and x = 8. If the straight line passing through the point (a,k) and parallel to the Y-axis divides the area A into two parts in the ratio 4:5, find the value of a .

Appreciate your efforts.  Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Area using definite integrals ! please help !

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Area using definite integrals ! please help !

hi Ansh

Welcome to the forum.

Hopefully the diagram below will help.  I have NOT attempted to show the green line in its correct position!

Firstly, you have got to use integration to calculate the area under the curve between the red lines.

Then my green line at x = a, splits the area into two parts in the ratio 4:5.  k is not needed in this question.

You need to use the same technique to get the area from 4 to 'a'  and set this equal to 4/9 of your first answer.  Solve for 'a'.

Hope that helps.

Bob

ps. Hello bobbym.  Sorry I've been away from the forum.  I've been travelling in New Zealand.  And on 7 Feb I became a grandfather!

Last edited by Bob (2012-02-14 02:52:27)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Area using definite integrals ! please help !

Hi Bob;

I know that. Congratulations about being a grandfather! Boy or girl?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Area using definite integrals ! please help !

hi bobbym,

We've known it would be a boy ever since the scans.  Named James.

I'll check to see if my daughter is happy for me to post a picture.  Since she has posted everything on Facebook already it will probably be allowed.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Area using definite integrals ! please help !

Hi Bob;

You may have told me that and I just forgot it. Congratulations again for a grandson! Post a picture if you can.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ansh Agrawal

Member

Registered: 2012-01-26

Posts: 11

Re: Area using definite integrals ! please help !

hi bob..
thanks a tonne for your useful help..

m facing problem in just one thing. and that's drawing this given graph.. how do i do that ? please help me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Area using definite integrals ! please help !

hi Ansh Agrawal

Sorry I missed this reply before.

If you just want to find out what a graph looks like then go to:

http://www.mathsisfun.com/data/function … =-8&ymax=8

But if you need to be able to sketch graphs for yourself without any aids have a look at

http://www.mathisfunforum.com/viewtopic … 29#p166429

especially post #7 where I have given a pretty comprehensive list of things to do when trying to sketch a graph.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob