Help Need to integrate to the arcsin(u) but don't know how

Thread starter amnestic
Start date Feb 1, 2010
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Integrate

In summary, to integrate arcsin(u), you can use the trigonometric substitution method by letting u = sin(x) and using the formula for integrating u^n. The indefinite integral of arcsin(u) is 1/2(u*arcsin(u) + sqrt(1-u^2)) + C. Integration by parts is not suitable for integrating arcsin(u). Special techniques like trigonometric identities or u-substitution can be used to simplify the integral. The limits of integration for integrating arcsin(u) will vary depending on the problem and given values of u. It is important to carefully read the problem and determine the appropriate limits of integration before solving the integral.

Feb 1, 2010

amnestic

Evaluate the integral:

(dx)(17x-x^2)^(-1/2)

...no clue

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Feb 1, 2010

sutupidmath

for the arcsine, try integration by parts!

Feb 1, 2010

amnestic

I don't know how to do that...

can you show me the steps?

Feb 2, 2010

vela

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Complete the square inside the radical.

1. How do I integrate arcsin(u)?

To integrate arcsin(u), you can use the trigonometric substitution method. Let u = sin(x), then du = cos(x)dx. Substituting these values into the integral, you will end up with an integral in terms of u. You can then use the formula for integrating u^n to solve the integral.

2. What is the indefinite integral of arcsin(u)?

The indefinite integral of arcsin(u) is 1/2(u*arcsin(u) + sqrt(1-u^2)) + C.

3. Can I use integration by parts to integrate arcsin(u)?

No, integration by parts is not a suitable method for integrating arcsin(u) as it will lead to a more complex integral that cannot be easily solved.

4. Are there any special techniques for integrating arcsin(u)?

Yes, there are a few special techniques that can be used to integrate arcsin(u), such as using trigonometric identities or u-substitution. It is also important to simplify the integral as much as possible before attempting to solve it.

5. What are the limits of integration for integrating arcsin(u)?

The limits of integration will depend on the specific problem and the given values of u. It is important to carefully read the problem and determine the appropriate limits of integration before solving the integral.