We note that x 1 3 2 x 1 Therefore the following entry from the Table of Trigonometric Substitutions is appropriate Expression x

Question

We note that x 1 3 2 x 1 Therefore the following entry from the Table of Trigonometric Substitutions is appropriate Expression x a If x 1 x a then a 1 Submit x a sec 8 0 0 Substitution dx 12 12 X17 2 100 0 S sec 4 sec 8 tan 8 tan 8 0 1 or or 8 2 We also must make a substitution for the limits of integration in the definite integral Since x sec 0 we note that when x 2 0 sec 4 sec 8 tan e de tan 0 Skip you cannot come back sec 4 Jn 3 2 1 Step 2 We have determined that if we let x sec 8 then dx sec 8 tan 8 de on the interval sec 4 Applying the substitution gives us the following result 3 2 de n 3 To evaluate this trigonometric integral we put everything in terms of sin 0 and cos 8 Doing so gives the following result cos 8 Identity sec 0 1 tan 0 Therefore we can let x sec 0 so dx sec 0 tan 0 de tan 8 sec 8 de 3 TL 3 Further when x 4 8 sec 4

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