SOLUTION: I am trying to find the shaded area (using integration). The area is a triangle; no values are given other than 0; (the origin) and the equation listed is x+y=6

Algebra ->  Surface-area -> SOLUTION: I am trying to find the shaded area (using integration). The area is a triangle; no values are given other than 0; (the origin) and the equation listed is x+y=6       Log On


   

Question 941581: I am trying to find the shaded area (using integration).
The area is a triangle; no values are given other than 0; (the origin) and the equation listed is x+y=6

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
the graph of y = -x +6 forms a triangle with the x and y axis intersection points, see graph below
+graph%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+-x+%2B6%29+
the y axis intercept is (0, 6) and the x axis intercept is (6, 0)
integral of -x +6 = (-x^2/2) + 6x
to determine the area under the curve, we evaluate the integral at x = 0 and x = 6
integral = 0 at x=0
integral = -18 + 36 = 18 at x = 6
Area = 18 - 0 = 18
we can check our answer by using area of triangle formula
Area = (1/2) * b * h = (1/2) * 6 * 6 = 18
our answer checks