Calc 2 Integration Area Problem

In summary: It may help us understand where you went wrong and guide us in finding the correct solution. Also, as mentioned before, it may be easier to integrate with respect to x instead of y.
  • #1
Alexa
4
0

Homework Statement


Please help me solve the calc problem pictured!

Homework Equations


y=3-x^2 and y=x+1

The Attempt at a Solution


My attempt is in one of the photos!
 

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  • #2
Alexa said:

Homework Statement


Please help me solve the calc problem pictured!

Homework Equations


y=3-x^2 and y=x+1

The Attempt at a Solution


My attempt is in one of the photos!
Type the problem statement, and your solution. Your images are not readable on my devices, and so I am unable to help or give hints.

For more on this issue, see the post "Guidelines for students and helpers", by Vela.
 
  • #3
The region R is bounded by y=3−x^2 and y=x+1.
The area of the region can be found by integrating: integral from 1 to 2 ______dy + integral from 2 to 3 ______dy
For the first blank I had (sqrt(3-y))-(y-1) and for the second I had (sqrt(3-y)-2)
These are both wrong according to the system
 
  • #4
Alexa said:
The region R is bounded by y=3−x^2 and y=x+1.
The area of the region can be found by integrating: integral from 1 to 2 ______dy + integral from 2 to 3 ______dy
For the first blank I had (sqrt(3-y))-(y-1) and for the second I had (sqrt(3-y)-2)
These are both wrong according to the system

So, the problem statement is asking you to find the area the hard way; integrating with respect to ##x## would be a lot easier.

Anyway, to see the ##x##-limits in the ##y##-integrals, you should start by drawing a picture of your region. The first (vertically lower) region goes from a negative value of ##y## to a positive value, and for each such ##y##, from a smaller (sometimes negative, sometimes positive) value of ##x## to a larger value of ##x##---giving a positive ##x##-length. You have your first integral going from a large value of ##x## to a smaller one---giving a negative ##x##-length.

You seem to be assuming that ##x## must be positive, but that is not stated anywhere in the problem as you wrote it.
 
  • #5
Alexa said:
The region R is bounded by y=3−x^2 and y=x+1.
The area of the region can be found by integrating: integral from 1 to 2 ______dy + integral from 2 to 3 ______dy
For the first blank I had (sqrt(3-y))-(y-1) and for the second I had (sqrt(3-y)-2)
These are both wrong according to the system
Could you explain to us how you came up with your attempt?
 

1. What is the purpose of the "Calc 2 Integration Area Problem"?

The purpose of the "Calc 2 Integration Area Problem" is to calculate the area under a curve using integration techniques. This allows us to find the total area of a complex shape or region, which would be difficult to do using traditional geometric methods.

2. How is the "Calc 2 Integration Area Problem" different from other integration problems?

The "Calc 2 Integration Area Problem" typically involves finding the area between a curve and the x-axis, while other integration problems may involve finding the volume, length, or surface area of a three-dimensional object. Additionally, the "Calc 2 Integration Area Problem" often requires the use of more advanced integration techniques, such as integration by parts or substitution.

3. What are some common techniques used to solve the "Calc 2 Integration Area Problem"?

Some common techniques used to solve the "Calc 2 Integration Area Problem" include the fundamental theorem of calculus, the method of u-substitution, integration by parts, and trigonometric substitution. These techniques allow us to simplify the integration process and find the area under a curve more efficiently.

4. What are some real-world applications of the "Calc 2 Integration Area Problem"?

The "Calc 2 Integration Area Problem" has various real-world applications, such as calculating the volume of irregularly shaped objects, finding the work done by a variable force, and determining the center of mass of an object. It is also used in fields such as physics, engineering, and economics to solve problems involving rates of change and optimization.

5. How can I practice and improve my skills in solving the "Calc 2 Integration Area Problem"?

To improve your skills in solving the "Calc 2 Integration Area Problem," you can practice with various integration problems and work through them step by step. You can also seek help from a tutor or attend review sessions to better understand the concepts and techniques involved. Additionally, practicing with real-world applications of the "Calc 2 Integration Area Problem" can help you see the practical significance of this mathematical concept.

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