Engineering Board Exam Reviewer · Integration by Parts · medium

Evaluate: x2 ≤ft(x ),dx

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

Answer

D. - x2 ≤ft(x ) + 2 x ≤ft(x ) + 2 ≤ft(x )+C

Solution

Parts twice: x2 x,dx=-x2 x+2 x x,dx=-x2 x+2x x+2 x+C.

More Integration by Parts questions

  1. Evaluate: x ≤ft(2 x ),dx
  2. Evaluate: x3 x,dx (assume x>0)
  3. Evaluate: x,ex,dx
  4. Evaluate: x x,dx
  5. Evaluate: x,dx
  6. Evaluate: x2 ex,dx
  7. Evaluate: x (2x),dx
  8. Evaluate: x ≤ft(x ),dx (for 0<x<1)
  9. Evaluate: ≤ft( x ),dx (assume x>0)
  10. Evaluate: x3 ex2,dx

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