hi every one what is the scientific reason for using trigonometric compensation in integration? and what is the rule that we rely on in other compensation? (√(a^2 −x^2 ))→→x=a sin(θ) OR a cos(θ) (√(a^2 +x^2 ))→→x=a tan(θ) OR a cot(θ) (√(x^2 −a^2 ))→→x=a sec(θ) or a csc(θ)


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Question Number 91037 by M±th+et+s last updated on 27/Apr/20

$h i e v e r y o n e$ $w h a t i s t h e s c i e n t i f i c r e a s o n f o r u s i n g$ $t r i g o n o m e t r i c c o m p e n s a t i o n$ $i n i n t e g r a t i o n ?$ $a n d w h a t i s t h e r u l e t h a t w e r e l y o n$ $i n o t h e r c o m p e n s a t i o n ?$ $\sqrt{a^{2} - x^{2}} \to\to x = a s i n (θ) O R a c o s (θ)$ $\sqrt{a^{2} + x^{2}} \to\to x = a t a n (θ) O R a c o t (θ)$ $\sqrt{x^{2} - a^{2}} \to\to x = a s e c (θ) o r a c s c (θ)$
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