Find the volume of the solid obtained by rotating the region bounded by the given curves

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. 

y=x2x=y2 about the axis x=5 
May 1st, 2015

The domain bounded by the curves y = x2 and x = y2 can be described by the inequalities:

0 ≤ y ≤ 1, y2 ≤ x ≤ √(y). Then the volume can be expressed as the following integral:

V = π ∫01 [x22(y) – x12(y)] dy, where x2(y) = √(y) + 5 and x1(y) = y2 + 5.

Thus, V = π ∫01 [(√(y) + 5)2 – ( y2 + 5)2] dy =

π ∫01 [(y + 10√(y) + 25) – (y4 + 10y2 + 25)] dy =

π ∫01 [y + 10√(y) – y4 – 10y2 ] dy =

π ( y2/2 + (20/3)y√(y) – y5/5 – (10/3)y3 )]01 =

π ( 1/2 + 20/3 – 1/5 – 10/3) = π ( 1/2 + 10/3 – 1/5) = π ( 15 + 100 – 6)/30 = 109π/30.


May 1st, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
May 1st, 2015
...
May 1st, 2015
Oct 20th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer