Finding the integral of an improper fraction

In summary, the conversation discusses using substitution to find the integral of a given expression. The suggested method is to use long division to simplify the expression before finding the integral. The conversation ends with confirmation that the resulting expression should be integrated.
  • #1
howsockgothap
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0

Homework Statement



Use substitution to find the integral of (12x2 + X -12)/(3x - 2)


Homework Equations





The Attempt at a Solution



I know I need to use long division to work it down to a proper fraction. That is where my real problem lies. Using long division I get that (12x2+x-12)/(3x-2) is equal to 4x-3 with a remainder of -6. I don't really understand what that means in terms of my question, especially with the remainder. Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?
 
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  • #2
howsockgothap said:
Does this just mean that I have to find the integral of (4x-3) - 6/(3x-2)?

Yes, assuming that your long division is correct. You should know how to take the integral of (4x-3) - 6/(3x-2).
 
  • #3
right on, thanks.
 

1. How do you find the integral of an improper fraction?

The integral of an improper fraction can be found by first converting the fraction into a mixed number or whole number. Then, use the power rule or other integration techniques to find the antiderivative. Finally, evaluate the antiderivative at the upper and lower limits of integration and take the difference.

2. What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. This type of fraction cannot be simplified into a whole number or mixed number.

3. Is it possible to find the integral of an improper fraction?

Yes, it is possible to find the integral of an improper fraction using integration techniques such as the power rule, substitution, or integration by parts.

4. Can an improper fraction be converted into a proper fraction?

Yes, an improper fraction can be converted into a proper fraction by dividing the numerator by the denominator. The resulting fraction will have a whole number and a proper fraction as the numerator and denominator, respectively.

5. Why do we need to find the integral of an improper fraction?

Finding the integral of an improper fraction is necessary when solving problems in calculus, physics, and other fields that involve continuous change. It allows us to find the total change or area under a curve, which can have real-world applications.

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