Engineering Board Exam Reviewer · Integration by Substitution · medium

Evaluate: x 1 - x4,dx (for 0<x<1)

1. ≤ft(x2 )+C
2. ≤ft(x2 )2+C
3. ≤ft(x2 )4+C
4. - 1 - x42+C

Answer

B. ≤ft(x2 )2+C

Solution

Let u=x2, du=2x,dx. Then x,dxsqrt(1-x4)= 12 dusqrt(1-u2)= 12 (x2)+C.

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