What is the integral of 2x?

x² + C

Using the power rule ∫xⁿ dx = xⁿ⁺¹/(n+1) + C, ∫2x dx = 2 × x²/2 + C = x² + C.

Understanding Calculus questions

Calculus questions look at how quantities change. At the introductory level almost everything follows from the power rule plus the product, quotient and chain rules.

How to approach it

1. Rewrite roots and fractions as powers before differentiating.
2. Apply the power rule term by term, then chain rule for composite functions.
3. For integration, reverse the power rule and add the constant of integration.
4. Differentiate your integral back to confirm it returns the original expression.

Common mistakes to avoid

• Omitting + C in an indefinite integral.
• Applying the power rule to the exponent instead of the base.
• Skipping the inner derivative in the chain rule.

Where it appears: Core to CBSE Class 11–12, IB Mathematics AA, and A-level equivalents.