Question

Question 4: Find the volume of the solid obtained by rotating about the y-axis the region bounded by the curves x = 2 - y2 and x = y4

Answer 1

solution: Given, x 2-4 and -G 4 x=2-4² 3 !) tu -3 -2 3x 3 0 4 62 4 Graye -47 Intersection points of 2-g2 and ne equate both, we have 3-y²= y ye+4²220 ye+ 2y ² - 4 2 - 200 ye (y² + 2)-1(y + 2)=0 (y² + 2) (421) y?+2 y²-1 ~ (4+1) (y +)=0 y=-114=1 21

b where a = -1 b= 1 2 volume by washer method is given by v=tla (12 rundy St (2-4)= (y² gdy was (esyo ay " - yogay 2 [ 4 $ - $ I[ 8 + 2/3 - 3 - 2/3 I-HE 3 4 y [ dj ty 3. 4 I of 4 + VET 360t la 120 - 10 45 V=1TX and 45 ㅠ v- 240 45 Answer