Definite integral

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KindofSlow

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Mar 5, 2010
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Exercise:
Integral from 0 to 1 of 2/((4-x^2)^(1/2)) or 2/sqrt(4-x^2)
Book pulls out the 2 in the numerator and calculates arcsin(x/2) from 0 to 1 = pi/6.
Then multiplies by the 2 for a final answer of pi/3.

I factored out the 4 under the radical which becomes 2 in the denominator which cancels with the 2 in the numerator.
So now is i
ntegral from 0 to 1 of 1/((1-((x^2)/4))^(1/2)) or 1/sqrt(1-(x^2)/4)
F is still arcsin(x/2) from 0 to 1 = pi/6.
But I don't have the 2 to multiply by so pi/6 is my final answer.
Which is wrong.
But I cannot find my mistake.

Any assistance pointing out my mistake will be greatly appreciated.
Many apologies in advance if my mistake is something really stupid (which, unfortunately, seems highly likely at this point)
Thank you​
 
KindofSlow said:
Exercise:
Integral from 0 to 1 of 2/((4-x^2)^(1/2)) or 2/sqrt(4-x^2)
Book pulls out the 2 in the numerator and calculates arcsin(x/2) from 0 to 1 = pi/6.
Then multiplies by the 2 for a final answer of pi/3.

I factored out the 4 under the radical which becomes 2 in the denominator which cancels with the 2 in the numerator.
So now is i
ntegral from 0 to 1 of 1/((1-((x^2)/4))^(1/2)) or 1/sqrt(1-(x^2)/4)
F is still arcsin(x/2) from 0 to 1 = pi/6.
But I don't have the 2 to multiply by so pi/6 is my final answer.
Which is wrong.
But I cannot find my mistake.

Any assistance pointing out my mistake will be greatly appreciated.
Many apologies in advance if my mistake is something really stupid (which, unfortunately, seems highly likely at this point)
Thank you
​
Click to expand...
Can you please show us your exact work so we can pinpoint your mistake, especially how you made your substitution?
 
Aha!
That's it!
1/2 x = sin u
dx = 2 cos u du
I missed that now the 2 is back in there.
So it's 2 arcsin (x/2) (not just arcsin (x/2))

Thank you very much!
 
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