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Inverse trig functions

  • Thread starter alijan kk
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Homework Statement


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why this formula works ?

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The Attempt at a Solution


when i take the derivative of the right side ,,, there is an additional "a" in the numerator in place of 1,, why the derivative of arcsine of (u/a) not exactly same with the expression under the integral sign
28217670_236535466916604_1075396015_o.jpg
 

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  • #2
andrewkirk
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In order to finally perform the integration in the last step you need to do a substitution, say replacing ##u/a## by ##x## so that your integrand has the form ##1/\sqrt{1-x^2}##. In order to do that you need to make the other changes that are part of doing a variable substitution in integration. Those changes should cancel out the factor ##1/a## and leave you with the nice, clean result you want.
 
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now i understand it very well,,,, thankyou for they reply
In order to finally perform the integration in the last step you need to do a substitution, say replacing ##u/a## by ##x## so that your integrand has the form ##1/\sqrt{1-x^2}##. In order to do that you need to make the other changes that are part of doing a variable substitution in integration. Those changes should cancel out the factor ##1/a## and leave you with the nice, clean result
 

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