Use integration to find the area of the triangle?

equations of the three sides:

y = -1 x + 4

y = x / 3

y = 3 x

Area = 4.0000

i will translate the triangle so as that the (2,-3) is (0,0): (0,0),(2,9),(4,4) there are 3 equations for the lines, y=9x/2 y=x and for the final one m=(9-4)/(2-4)=-5/2 y-4=-5/2(x-4) y=-5x/2+10+4=-5x/2+14 so combine with y=9x/2 over y=4 from 0 to 2 and y=-5x/2+14 over y=4 from 2 to 4 quite, making use of this equipment, i've got proved that a triangle with one verticie on the beginning and the different vercies at (a,b) and (c,d) has the section formulation: A=(one million/2)abs(det(row1(a,b),row2(c,d))) or in easy terms a=(one million/2)|advert-bc| so A=(one million/2)|2*4-4*9|=(one million/2)|8-36|=14 continous edit:fixing, finished ok for the easily integrals that are somewhat straightforward to do (of direction in admire to x): int(9x/2-x, from 0 to 2) + int(-5x/2+14-x from 2 to 4) =14