Question

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...

Answer 1

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

Answer 2

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?

Answer 3

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