Area enclosed by line and curve - integration

In summary, the concept of "area enclosed by line and curve" in integration involves calculating the total area between a given curve and a line on a graph. This is done using integration to find the definite integral of the function representing the curve. Integration is used because it allows for the calculation of areas of irregular shapes that cannot be measured using traditional geometric formulas. The steps involved in finding this area include identifying the function, setting up and solving a definite integral, and calculating the final result. Real-world applications of this concept include calculating distance, revenue/profit, land area, and volume in various fields.
  • #1
donjt81
71
0
Hi guys,

I need some help on this. It is in the integral section so I am assuming you use integrals for this. Can someone point me in the right direction.

Find the total area enclosed by the line x = -3 and the curve x = 2y - y^2
 
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  • #2
You have to take [tex] \int_{a}^{b} f(y) - g(y) \; dy [/tex] where [tex] f(x) [/tex] is the greater function. To get the limits of integration set [tex] - 3 = 2y-y^{2} [/tex]
 
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  • #3
so let me see if I understand this correctly.
[tex] \int_{-1}^{3} (2y-y^{2}) - (-3) \; dy [/tex]

is that correct?
 
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FAQ: Area enclosed by line and curve - integration

What is the concept of "area enclosed by line and curve" in integration?

The concept of "area enclosed by line and curve" in integration refers to the calculation of the total area between a given curve and a line on a graph. This is typically done by using integration to find the definite integral of the function representing the curve.

How is the area enclosed by line and curve calculated using integration?

The area enclosed by line and curve is calculated by finding the definite integral of the function representing the curve. This involves breaking the area into small rectangles and adding up the areas of these rectangles using the formula for the definite integral.

Why is integration used to find the area enclosed by line and curve?

Integration is used to find the area enclosed by line and curve because it allows for the calculation of the area of irregular shapes that cannot be measured using traditional geometric formulas. Integration allows for the breaking down of these shapes into smaller, measurable parts.

What are the steps involved in finding the area enclosed by line and curve using integration?

The steps involved in finding the area enclosed by line and curve using integration include: 1. Identifying the function representing the curve2. Setting up the definite integral with the appropriate limits of integration3. Solving the integral using integration techniques such as substitution or integration by parts4. Calculating the definite integral to find the area enclosed by the line and curve

What are some real-world applications of finding the area enclosed by line and curve using integration?

Some real-world applications of finding the area enclosed by line and curve using integration include: - Calculating the area under a velocity-time graph to determine the distance traveled by an object- Finding the area under a curve in economics to calculate the total revenue or profit of a business- Measuring the area of irregularly shaped land plots in surveying and land development- Determining the volume of an irregularly shaped object, such as a kidney stone, in medicine

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