Calculus - Integrals

Consider the region enclosed by the graphs of x=y^2-5 and x=3-y^2

a)Express the area of this region by setting up an integral with respect to x

b) Express the area of this region by setting up an integral with respect to y

c) Find the area of this region by evaluating one of the definite integrals found above

  1. 0
  2. 0
  3. 34
asked by Beth
  1. The curves intersect at (-1,2) and (-1,-2)

    So, using horizontal strips of width dy, the area is

    a = ∫[-2,2] (3-y^2)-(y^2-5) dy

    Using vertical strips, we have to split the region in two at the intersections, and then symmetry helps:

    a = ∫[-5,-1] 2√(x+5)dx
    + ∫[-1,3] 2√(3-x)dx

    1. 0
    2. 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two

    asked by mary on March 24, 2010
  2. math

    what is the area of the region enclosed by the graphs of y=2- lx-3l and y= x^2-2x?

    asked by cherry on February 28, 2011
  3. Calculus

    Let f(x)=x^3+3x and g(x=5x^2-x Determine the area of the region enclosed by the graphs of f and g.

    asked by Anonymous on November 22, 2011
  4. Calculus 1

    Let f be the function given by f(x)=3sqrt(x-2). A) On the axes provided sketch graph of f and shade the region R enclosed by the graph f, the x-axis, and the vertical line x=8 (already completed just mentioned it for part B.) B)

    asked by Michael on April 28, 2011
  5. 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

    asked by Vanessa on April 25, 2014
  6. 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

    asked by Vanessa on April 25, 2014
  7. 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

    asked by Mia on April 26, 2014
  8. 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

    asked by Vanessa on April 24, 2014
  9. 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

    asked by Vanessa on April 24, 2014
  10. calculus

    1. Let R be the region in the first quadrant enclosed by the graphs of y=4-X , y=3x , and the y-axis. a. Find the area of region R. b. Find the volume of the solid formed by revolving the region R about the x-axis.

    asked by Taeyeon on March 9, 2012

More Similar Questions