Calculus

posted by .

Find the total mass of the triangular region with coordinates (-1,0),(0,4),and (1,0). All lengths are in centimeters, and the density of the region is (x)=5+x grams/c^m2.


I know that to get the total mass i have to do density* lenght and ingegrate, but I don't know how to to it for a triangle...

  • Calculus -

    draw the triangle.

    Notice the base is horizontal frm -1,0 to 1,0

    write the equation for the two legs
    left leg: y=mx+b where m= (4/1)=4
    y=4x+b
    4=4*0+b or b=4

    integrating the left side..

    mass=INT y*(5+x)dx fro x=-1 to 0 do that inegral. Now on the right side, the leg equation is y=-4x+4
    same equation as above, integrate from x=0 to 1

    be certain in each area to use as y either (-4x+4) or y=(4x+4)

    add the two masses

  • Calculus -

    What I did was:

    INT (-1,0) (4x+4)(5+x) dx
    INT 4x^+36x+20
    I integrated and got (4/3)x^3+18x^2+20x
    and evaluated from -1 to 0 and got 10/3 g and then from 0 to 1 and got 118/3 grams added and got 128/3 g and that's not the answer. What am I doing wrong?

  • Calculus -

    (4x+4)(5+x) = 4x^2 + 24x + 20

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calc

    Find the mass of the triangular region with vertices (0, 0), (2, 0), and (0, 1), with density function p( x, y ) = x^2 + y^2. Im having trouble setting up this integral. This is what i came up with: 2 -.5x+1 S S (x^2 + y^2) dydx 0 …
  2. calculus

    could some body please check this for me?
  3. Calculus

    I know I posted this problem earlier but I don't think it will be seen anymore since it's almost at the end of the page: Find the total mass of the triangular region with coordinates (-1,0),(0,4),and (1,0). All lengths are in centimeters, …
  4. Calculus

    Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may …
  5. CALCULUS

    The masses of 10 books are found to be in an arithmetic sequence. If their total mass is 13 kg and the lightest book has a mass of 400 grams, what is the mass of the heaviest book?
  6. Math

    [Multivariable Calc] Let R be the region that is inside of the cardioid r=2 + cos(theta) and outside the circle r=2?
  7. CALC

    Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ(x, y) = 5(x + y) m=?
  8. Calc

    Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ(x, y) = 5(x + y) m=?
  9. Math

    Find center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ(x, y) = 5(x + y) mass=30 Find center of mass
  10. CALC

    Find center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ(x, y) = 5(x + y) mass=30 Find center of mass

More Similar Questions