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^(1/2)), y=4, and 2y +2x = 6

I keep getting an area around 21.3 but it is incorrect. Am I close?

Thank you!

1. 👍 0
2. 👎 0
3. 👁 51
1. odd that one function is written as

2y = 4√x

why not just y = 2√x ?

Anyway, assuming the functions are correctly written, the area is roughly triangular, with vertices at (-1,4),(1,2),(4,4)

Integrating along x, we need to divide it up into two regions, over [-1,1] and [1,4]

a = ∫[-1,1] 4 - (3-x) dx + ∫[1,4] 4 - 2√x dx
= (x + 1/2 x^2)[-1,1] + (4x - 4/3 x^(3/2))[1,4]
= 2 + 8/3
= 14/3

Integrating along y is easier, since we just subtract the left from the right:

a = ∫[2,4] y^2/4 - (3-y) dy
= y^3/12 + y^2/2 - 3y [2,4]
= 14/3

1. 👍 0
2. 👎 0
posted by Steve

Similar Questions

1. Calculus HELP plz

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=4x^1/2,y=5,2y+1x=5 Do you really mean "2y+1x=5" ? It is not customary to use the coefficient

asked by jimmy on May 5, 2007
2. Calculus

Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. integrate with either respect to x or y, then find area S

asked by saywhat on October 21, 2010
3. calcus

Sketch the regions enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. integrate with either respect to x or y, then find area S

4. calculus

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y, y=4sin(x), y=e^(7x), x=0, x=pi/2

asked by mon on September 5, 2011
5. 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

asked by Kathy on October 26, 2012
6. Calculus

Sketch the region enclosed by the curves x= 49-y^2 and x = y^2 - 49. Decide whether to integrate with respect to x or y. Then find the area of the region.

asked by Jason on February 9, 2015
7. math

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,y=x^2+3

asked by Philip on April 27, 2019
8. math

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=e^1x, y=e^4x, x=1

asked by Anonymous on November 9, 2012
9. Math- Calc

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=e^(4x), y=e^(6x), x=1

asked by Kristina on October 29, 2010
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. x+y^2=42, x+y=0

asked by Kelly on November 21, 2013
11. 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

asked by Amy on November 21, 2013

More Similar Questions