Evaluate ∫₀⁴ |x² − 4x + 3| dx.

Evaluate ∫₀⁴ |x² − 4x + 3| dx.

• A. 4
• B. 8/3
• C. 4/3
• D. 8

Answer: A) 4

Explanation: x² − 4x + 3 = (x−1)(x−3). Zeros at 1, 3. In [0,1]: positive. In [1,3]: negative. In [3,4]: positive. ∫₀¹ (x²−4x+3)dx + ∫₁³ −(x²−4x+3)dx + ∫₃⁴ (x²−4x+3)dx. Compute ∫(x²−4x+3)dx = x³/3 − 2x² + 3x. At 1: 1/3−2+3=4/3. At 0: 0. First part: 4/3. At 3: 9−18+9=0. At 1: 4/3. Second part: −(0 − 4/3) = 4/3. At 4: 64/3−32+12 = 64/3−20 = 4/3. At 3: 0. Third part: 4/3. Total = 4/3+4/3+4/3 = 4.