Question

What is the area under the curves of y=3, 2y=5(x)^1/2 and 2y+x=6

Answer 1

is there a picture attached?

Answer 2

Ah well it's just that graphing this is going to be a pain.. So let's see what we can do

Answer 3

no but I can attach one

Answer 4

if u can, please do so haha

Answer 5

k here it is

Answer 6

omg lol more of these webworks... i'm so sick of them haha

Answer 7

sorry

Answer 8

nah it's fine.. actually give the wolframalpha link, they also list the intercepts. it's easier.

Answer 9

http://www.wolframalpha.com/input/?i=Graph+y%3D3%2C+2y%3D5x^%281%2F2%29%2C+2y%2Bx%3D6

Answer 10

all right great thanks. Here we go..

Answer 11

So here I'm going to split the graph in two at the point where x+2y = 6 and 2y = 5sqrt(x) intersect

Answer 12

okay we did that

Answer 13

That's the upper limit of our first integral

Answer 14

okay

Answer 15

Sorry my browser's having trouble, anyway the upper intersect was 1. Now the lower intersect, which occurs when y =3 and 2y+x=6 intersect.

Answer 16

6+x=6, x = 0. So the first half of that area is:
Integral (upper curve - lower curve, 0,1)

Answer 17

how did you get one I got 1.36 doesnt it turn into a quadratic

Answer 18

x+5sqrt(x) = 6? Well I mean take a look, what number plus 5 times it's square root is 6?

Answer 19

okay i get it i never thought of it like that

Answer 20

Keep in mind, we're still calculating the first half. So now, the upper curve minus the lower curve (well they're lines, but whatever) is: 3 - (6-x)/2

Answer 21

So so far, the first half of our area is:
Integral (3 - (6-x)/2, 0,1)

Answer 22

Now let's find the 2nd half:
This time the lower limit is 1, because we are starting at one, and the upper limit is the intersection of y=3 and y = 5/2sqrt(x)

Answer 23

(5/2)*sqrt(x) = 3
sqrt(x) = 6/5 => x = 36/25

Answer 24

So 2nd integral is again, upper curve minus the lower curve from 1 to 36/25, or
Integral (3 - (5/2)*sqrt(x), 1, 36/25)

Answer 25

Calculate each integral and then add them to get 107/300 (lol I cheated, used wolf to compute)

Answer 26

so it is .356666667

Answer 27

Yea that looks right.

Answer 28

k i will try it and tell you if it works

Answer 29

it works thanks sooooo much you have no idea

Answer 30

np.