Question

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x", y = 5x, x2 0; about the x-axis V = Sketch the region. y у 5- 6 4 3 3 N -0. 0.5 1.0 X 1.5 -0.5 0.5 1.0 1.5

please answer 1&2

Answer 1

Soin 0 se? r20 y = 52 Ở find volume the solid obtained by rotating axis the region and abut Step-I Sketch the region = SP3 ở 5x. 3 5x² = Soc. 50% =0 0,0 -1, then y=5 y = ten and 512) - 10 X = ?, y = 5(21-40 intersection point 20 -1, y = 5 and x 20 Yous) 5 (1,5) 4 3 2 0.5

Step. I given by te volume v about the x- axis is dx. v - P - R ] Where a = 0 b-1 Ro=50 RI 5r3 so V = TT Scis (5x)?- 15x})? ] dz v=of '( 3522 - 0534 ] de 250[ x² V- 3 . 7 10) V: 25MTOT.CO + 1 (9" LA SA zsu[$-] 250[ 70 ] =7725 ,] Va 100 IT V- Volume V = 100 TT pi

y? - Qx, x=20 about y- quis. Shep. I Sketch the region. 2 = pr 1:२४ y y?- 2120) y? = 44 y = 4,0 y? 16 y - 4 then r = 11 2 intersection point 70-8, 7-9 4 (8,4) Х (8,0) o

Step-1 The volude v about the yo axis is given by . V = TT [ R - R where a=0 6=4 R2 = 84 Ri y² v-1650-499934 442_yt ] dy 4. da3 y5 V = TT f 7. * Чx S 4 V- TT گرم) [J. [xcuse ne - (0)2 + ] V: T (16) - Lowon] Min V. TT 512 T volume 15