# Calculus

posted by .

find the region enclosed by the given curves:

4x+y^2=9, x=2y

• Calculus -

I assume you want the area of the region

you will need their intersection
use substitution ....
4(2y) + y^2 = 9
y^2 + 8y - 9 = 0
(y-1)(y+9) = 0
y = 1 or y -9

if y = 1 , x = 2 --> (2,1)
if y = -9, x = -18 --> (-18, -9)

use horizontal slices
x = -(1/4)y^2 + 9/2
the value of x for the region
= (-1//4)y^2 + 9/2 - 2y

area = ∫(-1/4 y^2 + 9/2 - 2y ) dy from -9 to 1

= [(-1/20)y^5 + (9/2)y - y^2 ] from -9 to 1

= (-1/20) + 9/2 - 1 - ( (-1/20)(-59049) + 81/2 - 18)
= ....

you do the button - pushing.
(you might also want to check my arithmetic, my weakness)

## Similar Questions

1. ### Calculus

sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=5 rootx, y=5, and 2y+2x=7.
2. ### CALCULUS:)

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3sqrtx and y=3 and 2y+2x=5
3. ### Calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3sqrtx , y=3 , 2y+2x=5
4. ### Calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3(x^(1/2)) , y=5 and 2y+3x=6
5. ### Calculus-Area between curves

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=4*sqrt(x) , y=5 and 2y+4x=8 please help! i've been trying this problem the last couple days, even …
6. ### Calculus Area between curves

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 3y+x=3 , y^2-x=1
7. ### Calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. x+y^2=42, x+y=0
8. ### calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y=3 sqrt x,y=3 and 2y+1x=4
9. ### calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then find the area of the region. 2y = 4√x and y = 5 and 2y+2x = 6.
10. ### calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then ﬁnd the area of the region. y = 5x^2 and y = x^2+6

More Similar Questions