# 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)

• 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

## 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