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    I have a question from FP2, the topic about inverse trigonometric functions.

    \displaystyle\int \frac{1}{\sqrt{9 - 2x^2}} With limits 1.5 and -1.5.

    I got this to integrate to \left[arcsin(\frac{\sqrt{2}x}{3}) \right ] with limits 1.5 and -1.5, and with these coming out as 1.5 and -1.5 respectively, I get an answer of \frac{\pi}{2}. However my intergrating calculator gets an answer of 1.11....... I feel i'm right as it asks for an exact value for each of the integrals but why would the calculator give me something different?

    Could anyone confirm/refute my answer please?
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    (Original post by scillage)
    I have a question from FP2, the topic about inverse trigonometric functions.

    \displaystyle\int \frac{1}{\sqrt{9 - 2x^2}} With limits 1.5 and -1.5.

    I got this to integrate to \left[arcsin(\frac{\sqrt{2}x}{3}) \right ] with limits 1.5 and -1.5, and with these coming out as 1.5 and -1.5 respectively, I get an answer of \frac{\pi}{2}. However my intergrating calculator gets an answer of 1.11....... I feel i'm right as it asks for an exact value for each of the integrals but why would the calculator give me something different?

    Could anyone confirm/refute my answer please?
    You forgot to divide by root 2
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    (Original post by Indeterminate)
    You forgot to divide by root 2
    Why do I have to divide by \sqrt{2}? Is it because you have to have the x^2 coefficient as 1?
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    (Original post by scillage)
    Why do I have to divide by \sqrt{2}? Is it because you have to have the x^2 coefficient as 1?
    In the expression you're integrating, yes.

    \displaystyle \int \frac{1}{\sqrt{9-ax^2}} \ dx = \frac{1}{\sqrt{a}} \arcsin \frac{\sqrt{2} x}{3} + C

    You can verify this by differentiating the RHS
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    (Original post by Indeterminate)
    In the expression you're integrating, yes.

    \displaystyle \int \frac{1}{\sqrt{9-ax^2}} \ dx = \frac{1}{\sqrt{a}} \arcsin \frac{\sqrt{2} x}{3} + C

    You can verify this by differentiating the RHS
    Ok, thanks very much for your help
 
 
 
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