Sketch the region enclosed by the given curves. y = x^(1/2) , y = (1/3)x , x = 25

Answer 1

Answer 2

the parabola and line intersect at (0,0) and (9,3)

the integral of x^(1/2) - x/3 = 2x^(3/2)/3 - x^2/6

evaluated from 0 to 9

= 2(27)/3 - 81/6 = 18 -27/2 = 4 1/2 = area

then add the area = integral of x/3 - x^(1/2)

evaluated from x=9 to 25

= x^2/6 - 2x^(3/2)/3 from 9 to 25

= 625/6 - 2(125)/3 - (81/6 - 2(9))

= 34 1/3

total area = 34 1/3 + 4 1/2 = 38 5/6