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

Evaluate: 5 x - 3/≤ft(x - 1 ) ≤ft(x + 2 ),dx

1. 2 ≤ft|x + 2 |/3 + 13 ≤ft|x - 1 |/3+C
2. - 13 ≤ft|x + 2 |/3 + 2 ≤ft|x - 1 |/3+C
3. 13 ≤ft|x + 2 |/3 + 2 ≤ft|x - 1 |/3+C
4. 5 ≤ft(≤ft(x + 2 ) ≤ft|x - 1 | )2+C

Answer

C. 13 ≤ft|x + 2 |/3 + 2 ≤ft|x - 1 |/3+C

Solution

Write 5x-3/(x-1)(x+2)=A/x-1+B/x+2. At x=1: A= 23; at x=-2: B=13/3. Integrating gives 23 |x-1|+13/3 |x+2|+C.

More Partial Fractions and Rational Integrals questions

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

All Partial Fractions and Rational Integrals questions