Engineering Board Exam Reviewer · Partial Fractions and Rational Integrals · hard

Evaluate: 2 x2 + 3≤ft(x + 2 ) ≤ft(x2 + 1 ),dx

1. 11 ≤ft|x + 2 |/5 + ≤ft(x2 + 1 )10 + 2 ≤ft(x )5+C
2. 11 ≤ft|x + 2 |/5 - ≤ft(x2 + 1 )10 + 2 ≤ft(x )5+C
3. 11 ≤ft|x + 2 |/5 - ≤ft(x2 + 1 )5 + 2 ≤ft(x )5+C
4. 11 ≤ft|x + 2 |/10 - ≤ft(x2 + 1 )10 + 2 ≤ft(x )5+C

Answer

B. 11 ≤ft|x + 2 |/5 - ≤ft(x2 + 1 )10 + 2 ≤ft(x )5+C

Solution

Write 2x2+3/(x2+1)(x+2)=Ax+B/x2+1+C/x+2. At x=-2: C=11/5; matching coefficients gives A=- 15, B= 25. Integrating: - 110 (x2+1)+ 25 x+11/5 |x+2|+C.

More Partial Fractions and Rational Integrals questions

1. Evaluate: 3 x + 5≤ft(x - 1 )2 ≤ft(x + 1 ),dx
2. Evaluate: x2 + 1x ≤ft(x - 1 )2,dx (for x>1)
3. Evaluate: 1x2 ≤ft(x + 1 ),dx (assume x>0)
4. Evaluate: 5 x - 3/≤ft(x - 1 ) ≤ft(x + 2 ),dx
5. Evaluate: 1x4 + x2,dx (assume x>0)
6. Evaluate: 4 xx4 - 1,dx
7. Evaluate: x3 + 2x2 - 1,dx

All Partial Fractions and Rational Integrals questions