The area of the region (in sq. units), in the first quadrant bounded by the parabola y=9 x^2 and the lines x=0, y=1 and y=4 , is :

Step-by-step solution

aligned & Required area = _ y=1 ^4 y 9 d y & = 1 3 _ y=1 ^4 y^ 1 / 2 d y= 1 3 . 2 3 (y^ 3 / 2 ) |₁ ^4 & = 2 9 [ (4^ 1 / 2 )^3- (1^ 1 / 2 )^3 ]= 2 9 [8-1] aligned = 2 9 7= 14 9 sq. units.