Find the area?

Question

Find the area of the region in the first quadrant enclosed by the graph of y=x(1-x) and the x-axis. 

 

Answer: 1/6

 

Please show all work.

Answer 1

Y = X( 1-X = -X^2 +X

 

    1

  ∫ -X^2 + X =  - X^3/ 3 + X^2/2 =( - 1/3 + 1/2 ) - ( 0)

   0

                                                  = -1/3 + 1/2 = 1/6