Question

Question ( R ) is the region bounded by the functions ( f(x)=3 x^{2}+27 x+54 ) and ( g(x)=-frac{3 x^{2}}{2}-frac{27 x}{2}-27 ). Find the area ( A ) of ( R ). Enter an exact answer. Provide your answer below: [ A=square ext { units }^{2} ]

          Question
( R ) is the region bounded by the functions ( f(x)=3 x^{2}+27 x+54 ) and ( g(x)=-frac{3 x^{2}}{2}-frac{27 x}{2}-27 ). Find the area ( A ) of ( R ). Enter an exact answer.
Provide your answer below:
[
A=square 	ext { units }^{2}
]

$Question ( R ) is the region bounded by the functions ( f(x)=3 x^2+27 x+54 ) and ( g(x)=-frac3 x^22-frac27 x2-27 ). Find the area ( A ) of ( R ). Enter an exact answer. Provide your answer below: [ A=square ext units ^2 ]$

Added by Jovany S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

08/27/2023

Step 1

We do this by setting the two functions equal to each other and solving for $x$: \[3x^2 + 27x + 54 = -\frac{3x^2}{2} - \frac{27x}{2} - 27\] This simplifies to: \[ \frac{9x^2}{2} + \frac{81x}{2} + 81 = 0\] Dividing through by $\frac{9}{2}$ gives: \[x^2 + Show more…

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