Calculus

Consider the area between the graphs x+2y=4 and x+4=y2. This area can be computed
in two different ways using integrals

1) Compute as a sum of two integrals
2) Compute as a single integral
3) Either way, what is the area?

__

So for 1) I rewrote the two to be:
x = 4-2y
x = y^2-4
and setting them equal:
y^2-4 = 4-2y gives:
y^2+2y-8 or (y+4)(y-2)
Therefore the roots are y = -4 and 2

So if its the integral of f(x) from a to b plus the integral of g(x) from b to c:
a: -4, b: 0, c: -12
But what would be the functions f(x) and g(x)? Nothing I tried has worked, and I have no idea how to approach it as a single integral.

Thanks!

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. p.s. I wrote y2 for the second equation but it is y^2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. let's look at the graph
    http://www.wolframalpha.com/input/?i=plot+x%2B2y%3D4+and+x%2B4%3Dy%5E2

    You found the correct y values of the intersection points, the points are (0,2) and (12, -4)

    So why not take horizontal slices?
    the effective width = rightmost x - left x
    = (4 - 2y) - (y^2 - 4)
    = -y^2 - 2y + 8

    area = ∫ (-y^2 - 2y + 8) dy from -4 to 2
    = [ (-1/3)y^3 - y^2 + 8y] from -4 to 2
    = ( (-1/3)(8) - 4 + 16) - ( (-1/3)(-64) - 16 - 32)
    = -8/3 + 12 - 64/3 + 48
    = 36

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science

    X:22 Y:18 Z:18 Air will move from______. Área z to area y Área y to área z Área x to área z Área y to área X========

  2. Social studies

    What will happen in an area where large deposits of a desired mineral are found? Select the two correct answers. The area will experience a short term economic boom.*** Tourism in the area will increase in the short term People in

  3. Calculus

    Find the area of the region bounded by the graphs of y = 2 − x2 and y = −x.Find the area of the region bounded by the graphs of y = 2 − x2 and y = −x.

  4. Ap Calculus

    Find the area of the region bounded by the graphs of y=x, y=-x+6, and y=0

  1. math

    what happens to the area of a parallelogram when you double both the height and the base. A.the area is halved my answer B.the area is doubled C.the area is quadrupled D.the area is cut in half

  2. Calculus

    find the area of the region bounded by the graphs of y=-x^2+5x+2 and y=2

  3. math (9)

    Find the area of the region enclosed by these graphs and the vertical lines x = 0 and x = 3 f(x)=-x^2+2x+4 g(x)=-x+4

  4. Calculus

    What is the difference between "area" and "net area" in calculus? I'm doing homework dealing with definite integrals and some problems ask for area and some ask for net area. Thank you for your help in advance. 😀

  1. math (8)

    Find the area of the region enclosed by these graphs and the vertical lines x = 3 and x = 5 f(x)=x^2+5 g(x)=1

  2. Geometry

    Regular pentagons A and B are similar. The apothem of Pentagon A equals the radius of Pentagon B. Compare the areas. The area of Pentagon A is equal to 1.49 times the area of Pentagon B. The area of Pentagon B is equal to 1.49

  3. Math

    A rectangle has sides of 10 and 12 units.How can the area of a square be computed if it has the same perimeter of the rectangle?

  4. 6th G-Math

    1.What is a reasonable estimate for the area of a circle with radius 4 cm? A. Area=12cm^2 B. Area=16cm^2 C. Area=24cm^2 D. Area=48cm^2

View more similar questions or ask a new question.