Engineering Board Exam Reviewer · Trigonometric Integrals and Substitution · hard

Evaluate: 14 ≤ft(x ) + 5,dx (for -π<x<π)

1. 2 ≤ft(3 ≤ft(x/2 ) )3+C
2. ≤ft( ≤ft(x/2 )3 )3+C
3. 2 ≤ft( ≤ft(x/2 )3 )9+C
4. 2 ≤ft( ≤ft(x/2 )3 )3+C

Answer

D. 2 ≤ft( ≤ft(x/2 )3 )3+C

Solution

Use t= x2, x=1-t2/1+t2, dx=2,dt/1+t2: 2,dt/5(1+t2)+4(1-t2)= 2,dt/t2+9= 23 t3+C, so the result is 23 ≤ft( 13 x2 )+C.

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