Arc area...

F

Flic

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Joined
Dec 20, 2005
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How do i use integration to find the area of

f(x)=−23+16−(x−2)2\displaystyle f(x) = -2{\sqrt3} + {\sqrt {16 - (x-2)^2}}

It ranges from 0 to 4 on the x-axis.
I don't know how else to explain it, the whole problem is finding the area of a bulged triangle, and the bulge is that formula.
 
We have been doing some basic integration and I can do it perfectly fine, but the section we are working in has nothing to do with area/volume, so I can't quite put the two together yet, looking for just a touch of help. :)
 
First, you should note that f(0) = f(4) = 0, so that there are no issues with the SIGN of the area. When things cross the x-axis, it is sometimes rather confusing to the uninitiated.

Second, if you have not been introduced to Trigonometric Substitutions, you will not be able to do this one unless you are instructed to use various numerical methods, rectangles, trapezoids, something like that.

If you substitute: 4*sin(u) = (x-2), you should be in business.
 
tkhunny said:
First, you should note that f(0) = f(4) = 0, so that there are no issues with the SIGN of the area. When things cross the x-axis, it is sometimes rather confusing to the uninitiated.

Second, if you have not been introduced to Trigonometric Substitutions, you will not be able to do this one unless you are instructed to use various numerical methods, rectangles, trapezoids, something like that.

If you substitute: 4*sin(u) = (x-2), you should be in business.
Click to expand...


Do you think you could do it and walk me through? It was an example problem I missed and the next test has similar situations... My teacher is too busy to help. :\
 
tkhunny said:
If you substitute: 4*sin(u) = (x-2), you should be in business.
Click to expand...
Flic said:
Do you think you could do it and walk me through?
Click to expand...
How far have you gotten? Where are you stuck?

Please reply showing all of your steps, so the tutors can see where you are needing assistance.

Thank you.

Eliz.
 
You have 4*sin(u) = x-2.
You must find 4*cos(u) du = dx
Substitute those values into your expressions for x and dx and see what comes out.
 
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