SOLUTION: Let R be the region bounded by the curves y =root(x + 1 )and y = (x + 1)^2 . We will find the volume of the solid obtained by rotating R about the horizontal line y = &#8722;1.

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Question 1117974: Let R be the region bounded by the curves y =root(x + 1 )and y = (x + 1)^2
. We will find the
volume of the solid obtained by rotating R about the horizontal line y = −1.
(a) Find the points of intersection of the two curves.
(b) Sketch a graph of a portion of the curves, the region R, and the line y = −1.
(c) Calculate the volume of the solid obtained by rotating R about the horizontal line y = −1.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Points of Intersection

Two real roots, and

Points of intersection are and

Sketch

Volume of rotated around

Just slightly north of 3 cubic units. Verification of the antiderivative is left as an exercise for the student.

John

My calculator said it, I believe it, that settles it

SOLUTION: Let R be the region bounded by the curves y =root(x + 1 )and y = (x + 1)^2 . We will find the volume of the solid obtained by rotating R about the horizontal line y = &#8722;1.

SOLUTION: Let R be the region bounded by the curves y =root(x + 1 )and y = (x + 1)^2 . We will find the volume of the solid obtained by rotating R about the horizontal line y = −1.