# Editing Hint Applet (Trigonometric Substitution) Sample Problem

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