Question
Asked Dec 13, 2019
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Let R be the region in the xy-plane bounded between y= 4−x2
and y= 1+x2 . Set up an integral that is equal to the volume of the solid obtained by revolving R about the line x =−5. Do not evaluate the integral.
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Expert Answer

Step 1

First of all, consider the given equations.

 

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y = 4 –x .(1) ..... y =1+x? .(2) .... x =-5 -(3)

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Step 2

Now, find the intersection points of plots 1 and 2.

Solve the equation 1 and 2 by substitution method to get the x coordinates.

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-(1) y = 4 – x? y = 1+x? -(2) 4-x' = 1+x 4 - x - x =1+r² – x² 4 – 2.x? = 1 %3| 4 - 4- 2r = 1- 4 -2.r = -3 3 x = ±, ||

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Step 3

Then, put the value of x coordinate in equation ...

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y = 4 – x? .(1) ...... x = ±, Take x = y = 4 – 3 = 4 8– 3 3 5 =(-1.225, 2.5) (x; . V; ) = 3 5 =(1.225,2.5) 2 2 (x3, V ) = | %3D

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Tagged in

Math

Calculus

Integration