Applications of Integration

Find the area between f(y)=y(2-y) and g(y)=-y

Set functions equal to each other to get limits of integral.

f(y) = g(y)

y(2-y) = -y

2y - y2 = -y

y2 -3y = 0

y(y-3) = 0

y=0 or y=3

Integral of greater function minus the lesser.

∫[f(y)-g(y)]03dy

∫[y(2-y) - (-y)]03dy

∫[-y2 + 3y]03dy

[-y3/3 + 3y2/2]03

-33/3 + 3(3)2/2

-9 + 27/2

= 4.5

Study Sheet - Applications of Integration