Question

find the area of region of parabola at y square equal to 4 x and x square equal to 4

Answer 1

Answer:We have, y2 = 4ax --------------------------- (1)  

x2 = 4ay ---------------------------- (2)  

(1) and (2) intersects hence  

x = y2/4a (a > 0)  

=> (y2/4a)2 = 4ay  

=> y4 = 64a3y  

=> y4 – 64a3y = 0  

=> y[y3 – (4a)3] = 0  

=> y = 0, 4a  

When y = 0, x = 0 and when y = 4a, x = 4a.  

The points of intersection of (1) and (2) are O(0, 0) and A(4a, 4a).  

The area of the region between the two curves  

= Area of the shaded region  

= 0∫4a(y1 – y2)dx  

= 0∫4a[√(4ax) – x2/4a]dx  

= [2√a.(x3/2)/(3/2) – (1/4a)(x3/3)]04a  

= 4/3√a(4a)3/2 – (1/12a)(4a)3 – 0  

= 32/3a2 – 16/3a2  

= 16/3a2 sq. units.

Step-by-step explanation: