• Support PF! Buy your school textbooks, materials and every day products Here!

Area between a parabola and line?

  • #1

Homework Statement



Find the area of the region enclosed by the curves:
2y=sqrt(4x)
y=5 and
2y+3x=7

Homework Equations


A = integral from a to b of f(x)-g(x) dx


The Attempt at a Solution



Tried to integrate this with respect to y.
Found the intersection points to be y=2, -14/3
Then did the integral from -14/3 to 2 of (7/3 - 2y/3) - (1/4y^2)
My answer was 1000/81 but this is incorrect.
Also tried integral from -14/3 to 5 of (7/3 - 2y/3) - (1/4y^2)./
My answer was 841/324 but this was also incorrect.

Thanks to anyone who can help explain this to me, I'm so lost :s
 

Answers and Replies

  • #2
196
0
I would recommend you graph all those functions to give you an idea of where all the intersections are. For example y=(7-3x)/2 intersects y=5 in one place. Similarly y=(sqrt4x)/2 intersects y=5 in one place. And y=(7-3x)/2 and y=(sqrt4x)/2 intersect each other in one place. Your job is to sort out which integral to subtract from which to get at the area between all three functions. Hope this helps.
 
  • #3
33,514
5,195
In addition to what armolinasf said, the equation 2y = sqrt(4x) can be simplified to y = sqrt(x).

If you break up the region into vertical strips, you will need to use two integrals. If you break the region up into horizontal strips, you'll need only one integral.
 

Related Threads on Area between a parabola and line?

  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
10
Views
4K
Replies
2
Views
7K
Replies
6
Views
13K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
8K
Replies
22
Views
666
Replies
3
Views
4K
Replies
2
Views
917
Top