Evaluate ∫ (2x + 1) dx from 0 to 2.

The definite integral ∫ (2x + 1) dx from 0 to 2 equals 6

Step-by-Step Solution:
Find antiderivative: ∫(2x + 1)dx = x² + x + C
Apply definite integral formula: [x² + x]₀²
Substitute upper limit: (4 + 2)
Substitute lower limit: (0 + 0)
Calculate difference: 6 - 0 = 6

Key Mistake to Avoid: Students often forget to subtract the lower limit evaluation from the upper limit evaluation, only calculating one boundary value.



Quick Tip: When evaluating definite integrals, always write out the substitution clearly using square brackets [f(b) - f(a)] to avoid calculation errors.