Indefinite Integral: How to Use Trig Substitution?

Thread starter brandon hodoan
Start date Apr 19, 2015
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Indefinite Indefinite integral Integral

In summary, an indefinite integral is the process of finding the antiderivative of a function. This allows us to find a family of functions with the same derivative. To find the indefinite integral, we can use techniques such as the power rule, substitution, or integration by parts. The main difference between definite and indefinite integrals is that definite integrals have specific limits, while indefinite integrals have a general solution. It is important to find the indefinite integral as it helps us solve real-world problems and understand the behavior of a function. To check the correctness of our solution, we can take the derivative of the antiderivative and compare it to the original function or use online integral calculators.

Apr 19, 2015

brandon hodoan

Homework Statement

Find the indefnite integral using trig substitution.
∫[(x^2) / (1+x^2)]dx

Homework Equations

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The Attempt at a Solution

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Apr 20, 2015

Delta2

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Gold Member

The denominator should be ##sec^2(\theta)## so all you left with is ##\int tan^2\theta d\theta##. To calculate that make the substitution ##x=tan\theta## and notice that ##dx=(1+tan^2\theta)d\theta##.

What is the definition of an indefinite integral?

An indefinite integral is an operation that involves finding the antiderivative of a function. It represents a family of functions that have the same derivative.

How do you find the indefinite integral of a function?

To find the indefinite integral of a function, you can use integration techniques such as the power rule, substitution, or integration by parts. These techniques help you find the antiderivative of the function.

What is the difference between definite and indefinite integrals?

The main difference between definite and indefinite integrals is that definite integrals have a specific range of values for the independent variable, while indefinite integrals do not. In other words, definite integrals have upper and lower limits, while indefinite integrals are represented by a general solution.

Why is it important to find the indefinite integral of a function?

Finding the indefinite integral of a function is important because it allows us to solve various real-world problems, such as finding the area under a curve or calculating the work done by a force. It also helps us understand the behavior and properties of a function.

How can I check if my solution for the indefinite integral is correct?

You can check the correctness of your solution by taking the derivative of the antiderivative you found. If the derivative matches the original function, then your solution is correct. You can also use online integral calculators to verify your result.