For each problem, find the volume of the solid that results when the region enclosed by the curves isrevolved about the given axis.3) y=√x+1y=x² +1Axis: y = -16 +44) x=-y² + 2x = yAxis: x=-2Scanned with CamScanner

Answered: For each problem, find the volume of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

For each problem, find the volume of the solid that results when the region enclosed by the curves is
revolved about the given axis.
3) y=√x+1
y=x² +1
Axis: y = -1
6 +4
4) x=-y² + 2
x = y
Axis: x=-2
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Expert Solution

Step 1

As per company guidelines we are allowed to solve one question at a time so i am solving first one please resubmit for remaining questions. thank you.

Consider the given curves,

$y = \sqrt{x} + 1$ and $y = x^{2} + 1$

here we need to determine the volume of the solid when the region enclosed by the curves is rotated about the $y = - 1$ .

So, the diagram will be,

Now the intersection of the curves will be,

$\begin{array}{rcl} \sqrt{x} + 1 & = & x^{2} + 1 \\ \sqrt{x} & = & x^{2} \\ x - x^{4} & = & 0 \\ x (1 - x^{3}) & = & 0 \\ x & = & 0 or x = 1 \end{array}$