Editing Hint Applet (Trigonometric Substitution) Sample Problem

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SOLUTION(EV3(<<'END_SOLUTION'));
 
SOLUTION(EV3(<<'END_SOLUTION'));
 
$BBOLD Solution: $EBOLD $PAR
 
$BBOLD Solution: $EBOLD $PAR
To evaluate this integral use a trigonometric
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To evaluate this integral use a trigonometric substitution. For this problem use the sine substitution. \[x = {$a}\sin(\theta)\]
substitution. For this problem use the sine
 
substitution. \[x = {$a}\sin(\theta)\]
 
   
 
$BR$BR
 
$BR$BR
Before proceeding note that \(\sin\theta=\frac{x}{$a}\),
 
  +
Before proceeding note that \(\sin\theta=\frac{x}{$a}\), and \(\cos\theta=\frac{\sqrt{$a2-x^2}}{$a}\). To see this, label a right triangle so that the sine is \(x/$a\). We will have the opposite side with length \(x\), and the hypotenuse with length \($a\), so the adjacent side has length \(\sqrt{$a2-x^2}\).
and \(\cos\theta=\frac{\sqrt{$a2-x^2}}{$a}\). To see this,
 
label a right triangle so that the sine is \(x/$a\). We will
 
have the opposite side with length \(x\), and the hypotenuse
 
with length \($a\), so the adjacent side has length
 
\(\sqrt{$a2-x^2}\).
 
   
 
$BR$BR
 
$BR$BR

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