Question

Question 3 Evaluate ydA where R is the region bounded by y' = 4x and x'- R (10 marks)

Answer 1

6 x 4y 5 u 1494) w centre at (0,0) and Gole y²= 4x is a parabola Centree at 10,0) and Symmetric to positive X-axis and x? 44 YS also a parabola 2 1 1 X -5 -4 -3 2 - 1 1 2 3 u 5X .2 3 Symmetric to positive Y-axis. -4 -5 y² 4x Now, Solving y² 4x and ²44 Wehave, x ²44 у? 2 * (y² 4 y yz= 4x = X = 4 y ya 44 16 => ya = 644 → 94 - 64 4 - 0 →y (4364)=0 .: Eithere y = 0 Ove y3-64 = 0 » y3 =64 43 =) y = 4 =) ys 0 => x = 0 .. If y=0 then x² = uxo If y=4 then x²=16 =>x=4 ,: The point of interesection of y? 4x and x3 4y is (0,0) and (4,4)

4 vux . Slyda = j jy dy dx x=0 y = x2 / R 4 2x es y dx 2 X x=0 9 4. 4 = 2 et u dx 0 4 2 rese) ( ) } 2x $144 Fox 5}={ 1 2 [{2 x 16 - 10 24 } - o à [ ] x 5 16.5 2 0 o = all 2 (4) (4) 2 4.0 2 80 80 5 48 5 Slyda = 48 5 R have * Feel free to ask if you any doubt regareding the solution. Please upvote (like) if you understood the solution 2)