Calculating the Bounded Area of cos[x] from 0 to pi

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In summary, the conversation discusses a problem involving the area bounded by the curve cos[x] within ranges of pi and 0. Integration is suggested as a solution, and the person is advised to draw the graph and possibly break up the integration into two parts. The conversation ends with a request for more information about the problem.
  • #1
mathelord
what is the area bounded by the curve cos[x] within ranges of pi and 0
 
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  • #2
Sounds like a good problem. Have you tried doing anything with it?
 
  • #3
one word:"integration" use that ;)
 
  • #4
Draw the graph for cos[x] , and use integration from 0 to pie. After drawing the graph , see if you need to break up integration into two parts depending if the graph cuts the x-axis or not.

BJ
 
  • #5
what eventually becomes the answer
 
  • #6
Why don't you work it out yourself? After all, it is your homework problem, is it not? If you just want to check your work, you could post your work...
 
  • #7
it's no h/work,i just posted it here.pls what will the answer be
 
  • #8
I hope this isn't homework! I'ts very badly phrased if it is. The curve y= cos(x) doesn't "bound" any area and, since y is negative for x> [tex]
\frac{\pi}{2}[/tex], it's not clear what area you are talking about.

How about giving us more information about exactly what question you are asking. How did this problem come up?
 
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  • #9
It could be 0 or 2, depending on the context of the problem. :tongue2:
 

1. How do you calculate the bounded area of cos[x] from 0 to pi?

The bounded area of cos[x] from 0 to pi can be calculated using the formula: Area = ∫cos[x] dx = sin[x] + C, where C is the constant of integration.

2. What is the significance of calculating the bounded area of cos[x] from 0 to pi?

Calculating the bounded area of cos[x] from 0 to pi can help in understanding the behavior of the cosine function in this interval. It can also be used to solve various mathematical problems and applications in physics and engineering.

3. How does the bounded area of cos[x] from 0 to pi relate to the unit circle?

The bounded area of cos[x] from 0 to pi is equal to the x-coordinate of the point on the unit circle with an angle of pi. This is because the cosine function represents the x-coordinate of a point on the unit circle at a given angle.

4. Can the bounded area of cos[x] from 0 to pi be negative?

Yes, the bounded area of cos[x] from 0 to pi can be negative if the function is below the x-axis in this interval. This indicates that the net area is decreasing rather than increasing.

5. How can the bounded area of cos[x] from 0 to pi be visualized?

The bounded area of cos[x] from 0 to pi can be visualized by plotting the graph of the cosine function from 0 to pi on a graphing calculator or software. The bounded area is represented by the shaded region between the curve and the x-axis.

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