A definite integral has limits, like ∫₁⁴. Integrate, then substitute the top limit and subtract the value at the bottom limit. The constant c cancels, so leave it out.
∫₁⁴ (3x² + 2) dx = [x³ + 2x]₁⁴ = (64 + 8) − (1 + 2) = 69. Square brackets show the integrated expression with the limits. Take care with negative bottom limits and with fractional powers such as √x = x^(1/2).
Worked example
Evaluate ∫₋₂⁰ (5x − 4) dx.
- Integrate: [5x²/2 − 4x].
- At 0: 0. At −2: 10 + 8 = 18. So 0 − 18.
Answer:−18
Key words
- limits
- the numbers on the integral sign
- evaluate
- work out a number
- [ ]
- brackets showing the integrated function with limits
Practise this
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