Study guides › Level 10 · Calculus

Antiderivatives (going backwards)

Level 10 · Calculus · for questions like “Which function has the derivative 6x² + 4x − 3?”

💡 The idea

An antiderivative undoes a derivative: raise each power by one, then divide by the new power. Add + C, because any number on its own would have disappeared.

✏️ Worked examples

1. 6x² + 4x − 3: 6x² → 2x³, 4x → 2x², and −3 → −3x. So the answer is 2x³ + 2x² − 3x + C.

2. 9x² − 2: 3x³ − 2x + C.

⚠️ Watch out

• Check by taking the derivative of your answer. You should get back where you started.
• Divide by the new power, not the old one: x² → x³/3.

🎯 Try these

1. 3x² + 2x
2. 12x² − 6x + 1
3. 8x + 5

Answers: 1) x³ + x² + C 2) 4x³ − 3x² + x + C 3) 4x² + 5x + C

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.