Question

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12.

Answer 1

4y = 3x² is parabola upward 

line 2y = 3x +12

x	0	2	-2
y	6	0	3

They meet at pts (4, 12) and (-2, 3) 

4y = 3x² 

putting 2y = 3x +12 in it 

2(3x + 12) = 3x²

Required area (shaded) = Area under line 2y = 3x + 12 from x = - 2 to x = 4 – Area under parabola 4y = 3x² from x = -2 to x = 4