Study guides › Level 10 · Calculus

Definite integrals

Level 10 · Calculus · for questions like “What is the integral of (2x + 3) from x = 0 to x = 4?”

💡 The idea

∫ from a to b of f(x) = F(b) − F(a), where F is an antiderivative of f.

✏️ Worked examples

1. (2x + 3) from 0 to 4: F(x) = x² + 3x. F(4) − F(0) = 16 + 12 = 28.

2. 3x² from 1 to 3: F(x) = x³. 27 − 1 = 26.

3. 4x³ from 0 to 2: F(x) = x⁴, so 16.

⚠️ Watch out

• Top minus bottom, in that order.
• No + C needed here. It cancels out.

🎯 Try these

1. (2x + 1) from 0 to 3
2. 3x² from 2 to 4
3. 4x³ from 0 to 3

Answers: 1) 12 2) 56 3) 81

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