integral with (sin x)^4

Question

zamri 2013-7-12

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https://ww2.mathworks.cn/matlabcentral/answers/81836-integral-with-sin-x-4

Hi, i'd appreciate if anybody could help.

I am trying to integrate this function from 0 to 0.2985

    x = linspace(0,0.2985,1000);
    y=1/sqrt((1-power(sin(x),4)\0.0865^2));
    simps(x,y)

simps(x,y) is a another function that will calculate the integral of y over x. For some reason, when I change the division of linspace (say from 1000 to 500), the result of the simps(x,y) changes significantly.

I think there is something wrong with the line x = linspace(0,0.2985,1000); I don't know to change that line to what.

function simps(x,y) is verified correct by integrating other functions already. It is integration by simpson rule. I have tried double, quad, quad8 but unsuccessful.

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Answer 1

Mike Hosea 2013-7-12

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You have two errors. One, you need 1./sqrt instead of 1/sqrt. Second, you have \0.0865^2 instead of /0.0865^2. Here is how to define an anonymous function.

>> f=@(x)1./sqrt((1-power(sin(x),4)/0.0865^2));
>> integral(f,0,0.2985)
ans =
   0.390930321219332

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zamri 2013-7-12

ops, I'm sorry, I suppose I'll just try it in 2012a. thanks Sir.

Mike Hosea 2013-7-12

You can substitute quad or quadl there in an earlier release. I don't like to use these functions in my answers because QUAD and QUADL are now deprecated. You can also use QUADGK.

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