Engineering Board Exam Reviewer · Integration by Substitution · easy

Evaluate: ≤ft(x )≤ft( ≤ft(x ) + 1 )3,dx

1. 12 ≤ft( ≤ft(x ) + 1 )2+C
2. - 12 ≤ft( ≤ft(x ) + 1 )2+C
3. - 1≤ft( ≤ft(x ) + 1 )2+C
4. - 14 ≤ft( ≤ft(x ) + 1 )4+C

Answer

B. - 12 ≤ft( ≤ft(x ) + 1 )2+C

Solution

Let u=1+ x, du= x,dx. Then u-3,du=-1/2u2+C=-1/2(1+ x)2+C.

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