Engineering Board Exam Reviewer · Trigonometric Integrals and Substitution · medium

Evaluate: x2 4 - x2,dx (for 0<x<2)

1. x 4 - x22 + 2 ≤ft(x/2 )+C
2. - x 4 - x22 + 4 ≤ft(x/2 )+C
3. - x 4 - x22 + 2 ≤ft(x/2 )+C
4. - x 4 - x24 + ≤ft(x/2 )+C

Answer

C. - x 4 - x22 + 2 ≤ft(x/2 )+C

Solution

Let x=2 , dx=2 ,d , sqrt(4-x2)=2 . Then x2sqrt(4-x2)dx=4 2 ,d =2 - 2 +C=2 /2- xsqrt(4-x2)2+C.

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