Whats the intergral of sqrt(25-9x^2)?

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SUMMARY

The integral of sqrt(25-9x^2) can be solved by factoring out 25 from under the radical and applying trigonometric substitution. Specifically, one approach involves factoring out 9 to rewrite the expression as (1/3)*sqrt(25/9 - x^2) before using trigonometric substitution techniques. After obtaining the antiderivative, it is advisable to verify the result using the Wolfram Alpha integral calculator. The term "intergral" is incorrectly used; the correct term is "integral."

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Whats the intergral of sqrt(25-9x^2)?
 
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Factor out a 25 from under the radical and use trig substitution.
 


rochfor1 said:
Factor out a 25 from under the radical and use trig substitution.
I would factor out 9 from under the radical to give 1/3*sqrt(25/9 - x^2) and use trig substitution. After I got the antiderivative I might then go to the Wolfram site to check my result against theirs.
 


BTW, there is no such word as "intergral."
 


Mark44 said:
BTW, there is no such word as "intergral."
Nonsense.

The intergral, or rather, in German, Der Inter-Graal, was the cup Jesus drank from in the wedding in Kanaan(?) where he made water into wine.

This to distinguish it from the grail, or Der Graal, the cup he drank from at the last Supper.
 


OK, let me be more specific: there's no such word as "intergral" in English. And it appears that there is no such word in German, either. Inter-Graal != intergral.:smile:
 

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