Calculating the Area of a Circle in the First Quadrant | Integration Homework

In summary, the integral -8\int^{3}_{0}\sqrt{9-x^2}dx represents the area of a quarter circle in the first quadrant, and its value is -18\pi. This can be deduced from the shape of the integral and can also be calculated using a trigonometric substitution.
  • #1
gtfitzpatrick
379
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Homework Statement


-8[itex]\int^{3}_{0}\sqrt{9-x^2}dx[/itex]

Homework Equations


The Attempt at a Solution



am i right in thinking this the area of a circle in the first quadrant so my answer is-8([itex]\frac{9\pi}{4})[/itex] = -18[itex]\pi[/itex]

Thanks for reading?
 
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  • #2
gtfitzpatrick said:

Homework Statement


-8[itex]\int^{3}_{0}\sqrt{9-x^2}dx[/itex]


Homework Equations





The Attempt at a Solution



am i right in thinking this the area of a circle in the first quadrant so my answer is-8([itex]\frac{9\pi}{4})[/itex] = -18[itex]\pi[/itex]

Thanks for reading?

Sure it is.
 
  • #3
Dick said:
Sure it is.

Hi Dick.
thanks for reply but...
are you saying "it sure is" or are you asking "are you sure it is?"

"sure it is" is the way my friends would sarcastically say "your wrong":confused:
 
  • #4
gtfitzpatrick said:
Hi Dick.
thanks for reply but...
are you saying "it sure is" or are you asking "are you sure it is?"

"sure it is" is the way my friends would sarcastically say "your wrong":confused:

It's the not sarcastic 'it sure is'. The integral is -18*pi and you can deduce that from its being a quarter circle. You could also do it with a trig substitution and get the same thing.
 
  • #5
thanks a million Dick. :smile:
 

FAQ: Calculating the Area of a Circle in the First Quadrant | Integration Homework

What is the definition of integration of a circle?

The integration of a circle is a mathematical process that involves finding the area under a curve that represents the circumference of a circle. It is used to calculate the area of a circle or to solve problems involving circular motion.

What is the formula for integrating a circle?

The formula for integrating a circle is ∫ 2πr dx, where r is the radius of the circle and dx represents the infinitesimal width of the curve. This formula is derived from the circumference formula of a circle, C=2πr, and the definition of integration.

How is the integration of a circle different from the integration of other shapes?

The integration of a circle is unique because it involves a non-linear curve, unlike other shapes such as rectangles or triangles which have straight sides. This requires specific integration techniques, such as substitution or trigonometric substitution, to solve the integral.

What are some real-life applications of the integration of a circle?

The integration of a circle has many real-life applications, such as calculating the area of a circular field or the volume of a cylindrical tank. It is also used in physics and engineering to analyze circular motion and in calculus to solve problems involving the area under a curve.

How can I improve my skills in integrating circles?

To improve your skills in integrating circles, it is important to have a strong understanding of calculus and its principles. Practice solving various integration problems involving circles and familiarize yourself with different integration techniques. You can also seek help from a tutor or online resources for additional practice and guidance.

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