Determine the area of a region between two curves defined by algebraic functions

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  • #1
sgalos05
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R is the region bounded by the functions f(x)=3√x−4 and g(x)=3x/5−8/5. Find the area A of R. Enter answer using exact values.
 

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  • #2
jonah1
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Beer soaked query follows.
R is the region bounded by the functions f(x)=3√x−4 and g(x)=3x/5−8/5. Find the area A of R. Enter answer using exact values.
What have you done so far?
 
  • #3
Greg
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R is the region bounded by the functions f(x)=3√x−4 and g(x)=3x/5−8/5. Find the area A of R. Enter answer using exact values.

You need the roots $a,b$ of the equation $3\sqrt{x}-4=3x\sqrt{5}-\frac{8}{5}$

Once you have established these roots use them as endpoints in

$\int_{a}^{b}\left(3\sqrt{x}-4-3x\sqrt{5}+\frac{8}{5}\right)dx$

The result is the area $A$ of $R$.
 
  • #4
HOI
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Is the first first function $f(x)= \sqrt{x}- 4$ or $f(x)= \sqrt{x- 4}$?

Also I do not see the second function as $g(x)= 3x\sqrt{5}- \frac{8}{5}$. I see $g(x)= \frac{3x}{5}- \frac{8}{5}= \frac{3x- 8}{5}$.
 
  • #5
skeeter
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Just spitballin’ here ...

I would say $f(x) = 3\sqrt{x} - 4$ since it yields a simpler, nice solution when equating it to $g(x)$
 
  • #6
Greg
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Is the first first function $f(x)= \sqrt{x}- 4$ or $f(x)= \sqrt{x- 4}$?

Also I do not see the second function as $g(x)= 3x\sqrt{5}- \frac{8}{5}$. I see $g(x)= \frac{3x}{5}- \frac{8}{5}= \frac{3x- 8}{5}$.
yeah should have zoomed the page... lol... :)
 

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