Question

Find the area bounded by the curves x = 5 - y^2 and x - 2y = -5.

Answer 1

first, find out where two curves intersect so set them equal to each other and solve for x.

Answer 2

or you could solve for y and then find out the x value by plugging in.

Answer 3

okay I graphed it. I found where the curves intersect

Answer 4

(1,-2) and (5,0)

Answer 5

k now i plug that into an integral

Answer 6

Yeah. Remember area = top curve - bottom curve
your bounds are from x = 1 to x = 5

Answer 7

(12)-(12-8y)

Answer 8

does that look right?

Answer 9

nope

Answer 10

k let me try again

Answer 11

x = 5-y^2
x = 2y - 5

2y - 5 is the top curve
5-y^2 is the bottom curve
change it to a function of y
and then integrate it with respect to x

Answer 12

so I have to get y on one side of the equation. and the x's on the other and then integrate

Answer 13

yeah just change it

Answer 14

5 - x = y^2
sqrt(5-x) = y

x + 5 = 2y
(x+5)/2 = y

so the integral would be:
\[\int\limits_{1}^{5} (\frac{ x+5 }{ 2 } - \sqrt{5-x}) dx\]

Answer 15

I keep getting 10.66 but that is not the right answer.

Answer 16

hm, maybe integrate it with respect to y?

Answer 17

okay I will try that

Answer 18

the bounds will be different,

Answer 19

What will I change the bounds to?

Answer 20

will it be -2 to 0

Answer 21

the y coordinates

Answer 22

yeah

Answer 23

2y - 5 - (5-y^2) dy
integrate that from -2 to 0