Home » Ask & Discuss » Mathematics. » Integral Calculus « Back to Discussion

Integral Calculus

New kid on the Block

Joined:	27 Oct 2007
Post:	20

28 Oct 2007 19:23:12 IST

0 People liked this

505

Interesting area under curve question.

None

Find the area bounded by the curve x²+y²= 25, 4y = I 4-x² I and x = 0, above the x-axis ?

Solve the above question. Thank You.

Share this article on:

Comments (4)

Ramya Hegde

Blazing goIITian

Joined: 8 Feb 2007

Posts: 612

29 Oct 2007 02:13:31 IST

Like 0 people liked this

To get the total area, we can first calculate the area enclosed in the first quadrant, and then multiply by 2.

The point of intersection of the curve and the circle comes out to be (4,3) and (-4,3). We can consider only x=4 as we are calculating fr the first quadrant only.

Now,

for the function 4y = |4-x²|, it follows the graph of

y = 4-x² /4 for -2 <x<2

and

y= x² -4/4 for x<-2 and x>2

Hence to find the total area in the first quadrant, we first have to calculate area from 0 to 2, and then from 2 to 4 (i.e. where the parabola intersects the circle)

Hence A = 2[ _{[0 ]}^{[2 ]}{ 25 -x² - (4-x² /4) dx} +_{[2 ]}^{[4 ]} { 25-x² - (x²-4/4) dx } ]

= 2 [_{[0 ]}^{[ 4]} 25 -x² - _{[0 ]}^{[2 ]} (1-x²/4) -_{[2 ]}^{[4 ]} ( x²/4 -1) dx ]

On integrating u'll get,

A =2 [ 25/2. sin^-1 (4/5) +2 ]

= 25 sin^-1 (4/5) + 4

(sorry, couldn't post the graph)

Do tell me if i'm wrong

Cheerss!!

Rajat Dixit

New kid on the Block

Joined: 27 Oct 2007

Posts: 20

29 Oct 2007 09:20:18 IST

Like 1 people liked this

Sorry Ramya but answer is 25/2 sin inverse 4/5 + 2. Retry to get the same.

Ramya Hegde

Blazing goIITian

Joined: 8 Feb 2007

Posts: 612

29 Oct 2007 20:41:12 IST

Like 0 people liked this

I'm sorry,i had made a mistake while entering the limts. Thanx for pointing it out. I've edited my post. This is the area in the first quadrant.

astrojith

Blazing goIITian

Joined: 5 Jun 2007

Posts: 336

8 Nov 2007 20:59:02 IST

Like 0 people liked this

Could you please post the graph ? Please ... ?

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team