area between curves.

Sep 2008
631
2
I have attached the graph of the two equations, and I am suppose to find the area between them.

However I am not sure how to go about doing this, would it be the integral of the line minus the curve?

If so I keep getting the wrong answer.

Any help appreciated.

the equations are: \(\displaystyle y = 3 \) and \(\displaystyle y = \sqrt{x-2} \) and they intersect at the point \(\displaystyle 3 = \sqrt{x-2} \)
 

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Last edited:
Oct 2009
769
87
Before trying to figure this one

Would you suppose the origin figures into this problem?
 

Jester

MHF Helper
Dec 2008
2,470
1,255
Conway AR
Probably easiest to use horizontal rectangles. Hence

\(\displaystyle
\int_0^3 y^2 + 2\, dy.
\)
 
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Apr 2010
384
153
Canada
I have attached the graph of the two equations, and I am suppose to find the area between them.

However I am not sure how to go about doing this, would it be the integral of the line minus the curve?

If so I keep getting the wrong answer.

Any help appreciated.

the equations are: \(\displaystyle y = 3 \) and \(\displaystyle y = \sqrt{x-2} \) and they intersect at the point \(\displaystyle 3 = \sqrt{x-2} \)
\(\displaystyle A = \int_0^3 dy \int_0^{ y^2 + 2} dx \)

\(\displaystyle A = \int_0^3 ( y^2 + 2) dy \)

\(\displaystyle A = \frac{ y^3 }{3} |_0^3 + 6 \)

\(\displaystyle A = 9 + 6 = 15 \)