6.3LASolutions

# 6.3LASolutions - MthSc 108 Learning Activity Solutions...

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MthSc 108 Learning Activity Solutions Section 6.3: Volumes By Slicing and Rotation About An Axis For problems 1-5, find the volume for the solid generated by revolving the region bounded by 1. 2 1 () , 1 , 3 1 fx x x x == = + about the x-axis. 2 33 2 3 2 1 2 11 arctan arctan 3 arctan1 13 4 1 2 1 Vd x d x x x x ππ π ππ π  = = = =  +  + ∫∫ 2. 3/2 ,0 , 2 xy x y = about the y-axis. 2 22 4 2 3 00 0 4 4 y V y dy y dy = = 3. () s e c, () t a n, 0 , 1 xgx xx x = = about the x-axis. () () 1 1 0 0 sec tan tan 1 tan (1) Vx x d x x x d x d x x  =− = + = = =  x y x y x y

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4. () l n, 1 , fx xx x e == = about the y-axis. () () 1 11 22 2 2 2 2 00 0 1 2 y yy ee Ve e d y e e d y e y e ππ π   =− = = =     ∫∫ 5. 1 y = above and below by the curve sin , 0 / 2 yx x =≤ , and on the left by the y-axis, about the line 1 y = . () /2 2 2 0 0 1 sin 1 2sin sin 13 1 1 1 cos2 2cos sin 2 4 31 3 1 3 2 cos sin 0 2 cos0 sin 0 2 2 4 2 4 4 Vx d x x x d x d x x x x + + = +−
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6.3LASolutions - MthSc 108 Learning Activity Solutions...

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