Evaluation of Indefinite Integral

In summary, the conversation involves evaluating an indefinite integral and attempting to find the appropriate substitution. The suggested solution is to use the power rule to find antiderivatives for the given functions.
  • #1
futurept
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Homework Statement


Evaluate the following indefinite integral: (2t6-3)/t3 dt



The Attempt at a Solution


I know I need to substitute. Tried u= t3 and found du= 3t2dt. Tried to find where du would substitute in, but found nothing. Also tried u= 2t6-3. Found du=12t5dt and again cannot find where to sub in the du. Any suggestions on where I'm going wrong?
 
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  • #2
futurept said:

Homework Statement


Evaluate the following indefinite integral: (2t6-3)/t3 dt



The Attempt at a Solution


I know I need to substitute. Tried u= t3 and found du= 3t2dt. Tried to find where du would substitute in, but found nothing. Also tried u= 2t6-3. Found du=12t5dt and again cannot find where to sub in the du. Any suggestions on where I'm going wrong?

You don't need to substitute. [tex]\frac{2t^6 - 3}{t^3} = 2t^3 -3t^{-3}[/tex]. Now all you need to do is find antiderivatives for those two functions, using the power rule.
 
  • #3
Hey thanks for the help!
 

1. What is an indefinite integral?

An indefinite integral is a mathematical concept that represents the antiderivative of a function. It is used to find the original function that was differentiated to obtain a given function.

2. How is an indefinite integral evaluated?

An indefinite integral is evaluated by using integration techniques, such as substitution, integration by parts, and partial fractions. These techniques help to simplify the integral and make it easier to solve.

3. What is the difference between definite and indefinite integrals?

The main difference between definite and indefinite integrals is that a definite integral has specific limits of integration, while an indefinite integral does not. This means that a definite integral will give a numerical value, while an indefinite integral will give an expression with a constant of integration.

4. What is the purpose of evaluating an indefinite integral?

The purpose of evaluating an indefinite integral is to find the original function that was differentiated. This can be useful in many areas of mathematics and physics, such as finding the position of an object given its velocity or finding the probability density function of a random variable.

5. Can the value of an indefinite integral be negative?

Yes, the value of an indefinite integral can be negative. This can occur when the function being integrated has negative values or when the area under the curve is below the x-axis. In such cases, the indefinite integral will have a negative value, but it still represents the antiderivative of the given function.

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