Finding the Area Between Two Functions: Integration Problem from 0 to 2

In summary, the problem is to find the area between two functions on the interval from 0 to 2. The correct approach is to use the top function minus the bottom function. The graphs of the two functions cross at x=0, x=1, and x=2. The mistake was taking the wrong functions as "top" and "bottom".
  • #1
pb23me
207
0

Homework Statement


Find the area between f(x)=(x-1)^3 and f(x)=(x-1) on the interval from 0 to 2.


Homework Equations





The Attempt at a Solution

Working it out I am using the top function minus the bottom function from 0 to 1 and then from 1 to 2. The graphs cross at x=0,x=1,andx=2.
Im geting - (1/2) for my final answer and the answer is 1/2. It's been awhile since if done any calculus so I don't know why my answer is the wrong sign.
 
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  • #2
If you show us what you did, I'll be happy to point out what's wrong...
 
  • #3
Nevermind it will take me 30 mins of wasted time to type out all that goodbye
 
  • #4
pb23me said:
Working it out I am using the top function minus the bottom function from 0 to 1 and then from 1 to 2. The graphs cross at x=0,x=1,andx=2.
Im getting - (1/2) for my final answer and the answer is 1/2.

You took the wrong functions to "top" and "bottom". Plot them to see.

ehild
 
  • #5
That was what it was. Thanks
 

FAQ: Finding the Area Between Two Functions: Integration Problem from 0 to 2

What is a simple integration problem?

A simple integration problem is a mathematical problem that involves finding the integral of a function. The integral is a fundamental concept in calculus that represents the area under a curve. In simple integration problems, the function and the limits of integration are usually given, and the goal is to find the numerical value of the integral.

How do you solve a simple integration problem?

To solve a simple integration problem, you can use various techniques such as substitution, integration by parts, or trigonometric identities. The first step is to identify the function and the limits of integration. Then, you can choose the appropriate integration technique and apply it to find the integral. Finally, you can evaluate the integral to find the numerical value.

What are some common mistakes to avoid in simple integration problems?

Some common mistakes to avoid in simple integration problems include forgetting to apply the chain rule, making errors in integration by parts, and forgetting to include the constant of integration. It is also essential to carefully evaluate the integral and check for any arithmetic errors.

How can simple integration problems be useful in real-life applications?

Simple integration problems have many real-life applications, such as calculating the area under a curve in physics or engineering problems. They can also be used in economics to calculate the total cost or revenue of a business. In biology, integration can be used to model growth rates of populations. Overall, integration is a powerful tool for solving real-world problems.

Can integration problems become more complex?

Yes, integration problems can become more complex, especially when dealing with multivariable functions or improper integrals. In these cases, the techniques used to solve simple integration problems may not be applicable, and more advanced methods such as partial fractions or contour integration may be necessary. However, with practice and a good understanding of the fundamentals, these complex integration problems can also be solved effectively.

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