## Question

###### Immediate answers please Q9 (10 points) Let R be the region bounded by the curves *...

immediate answers please

Q9 (10 points) Let R be the region bounded by the curves * = y2 and y = 2 - x. Question 9, parts a) to c), are worth a total of 10 marks. Drop your files in the appropriate box. There are NO FILES to drop here. + Drag and drop your files or click to br Q9a (0 points) Sketch the region R. + Drag and drop your files or click to bro Q9b (0 points) Evaluate the volume when Ris rotated about the y-axis. + Drag and drop your files or click to brows Q9C (0 points) Evaluate the volume when Ris rotated about the line y = 2. + Drag and drop your files or Click to browse.

## Answers

Solution given the negion is bounded by uzy? and y= 2-2 31 (9) ar 0 -2 x=y2 y=2-2 yanis () Rotation about y= 2-2 za finding intens ection point a= 2-y x=y2 1 Ital) y2= -9 2 RCY) -21 ? y²+4-2=0 2 y² +29-4-2=0 29 (4+2)-1(9+2) = 7 (9+2) 19-1) =0 2 y=-2,1By washer method volume By Shell method rolume va s'= [(814))2-(199))J dy a Heal outer nadius Riyl=2-4 Innen nadius rcg)= y2 soi volume V =T S (2-4)? (y2, 2] dy -2 1 =T 4 + 4 .y?_ yy-go ] dy 2 = yy2 I (4y + 4 © Rotation abocet ya 2 گل 2 727 5 2 5 Height of the shell hey)=2-y-y 2 so Radius n(9) = 2-4 2 Irig) */*** 2a relys higdy 5(2-4)(2-y-y?) dy tu E y = 2-2 -27 72=2-4 hay2() 2ㅈ (Y-9}-uy+y) oly -2. - 3. 백 9 92 十9 2. y - 2 5 2 스

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