3. Find the area of the region bounded by ' 4y, y 2, y 4 and the >-axi

1.	3. Find the area of the region bounded by ' 4y, y 2, y 4 and the >-axisfirst quadrant.
Answer» The area can be found out by the integration of x = 2√y , from y = 2 to y = 4 so the integration is 2y^(3/2)/(3/2) = 4/3y^(3/2) now putting the limit we get area = (4/3)[4^(3/2) -2^(3/2)] = (4/3)[8-√8] = (32-8√2)/3 sq.units

3. Find the area of the region bounded by ' 4y, y 2, y 4 and the >-axisfirst quadrant.

Answer»

The area can be found out by the integration of x = 2√y , from y = 2 to y = 4

so the integration is 2y^(3/2)/(3/2) = 4/3y^(3/2)

now putting the limit we get area = (4/3)[4^(3/2) -2^(3/2)] = (4/3)[8-√8] = (32-8√2)/3 sq.units