Area Inside Circle x^2+y^2=a^2 Above b=7

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SUMMARY

The discussion focuses on calculating the area inside the circle defined by the equation x² + y² = a², specifically the area above the line y = b, where -a ≤ b ≤ a. Participants clarify that the task involves integrating or using geometric methods to find this area. The geometric approach is highlighted as simpler, utilizing the formula for the area of a triangle, A = ½ * u * v * sin(φ), where u and v are the sides of the triangle and φ is the angle between them.

PREREQUISITES
  • Understanding of the equation of a circle, specifically x² + y² = a²
  • Knowledge of basic integral calculus for area calculation
  • Familiarity with geometric principles, particularly the area of triangles
  • Ability to interpret inequalities involving variables, such as -a ≤ b ≤ a
NEXT STEPS
  • Study the geometric interpretation of areas within circles
  • Learn how to apply integral calculus to find areas under curves
  • Explore the properties of triangles and their areas in relation to circles
  • Investigate the implications of varying b within the constraints -a ≤ b ≤ a
USEFUL FOR

Students and educators in mathematics, particularly those focusing on geometry and calculus, as well as anyone interested in solving problems related to areas within circular boundaries.

wonguyen1995
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Find area inside circle x^2+y^2=a^2, above 7=b, -a \le b \le a ?? i think f of y right?
(-a to a) minus (-a to b)?
 
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wonguyen1995 said:
Find area inside circle x^2+y^2=a^2, above 7=b, -a \le b \le a
Maybe it's a typo and should read "above $y=b$". That is, find the area inside the circle $x^2+y^2=a^2$ that is located above the line $y=b$, where $-a\le b\le a$.

wonguyen1995 said:
?? i think f of y right?
(-a to a) minus (-a to b)?
Sorry, I don't understand your remark.
 
Evgeny.Makarov said:
Maybe it's a typo and should read "above $y=b$". That is, find the area inside the circle $x^2+y^2=a^2$ that is located above the line $y=b$, where $-a\le b\le a$.

Sorry, I don't understand your remark.

That is it, i mistake.
so can you help me??
 
Do you need a solution that uses integral? It's easier to find the area geometrically as described in Wikipedia using the fact that the area of a triangle with sides $u$ and $v$ and angle $\varphi$ between them is $\frac{1}{2}uv\sin\varphi$.
 

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