Key Formula
∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
Common Mistakes
- Forgetting + C on indefinite integrals — a very common and easily avoided point loss.
- Ignoring negative area below the x-axis — a definite integral counts it as negative, not positive.
- Applying the power rule when n = −1 instead of using the logarithm special case.
Frequently Asked Questions
What is the Fundamental Theorem of Calculus?
It links differentiation and integration, proving that integrating a function's derivative returns the original function — this is what makes definite integrals computable via antiderivatives rather than infinite sums.
What is u-substitution used for?
It reverses the chain rule, letting you integrate composite functions by temporarily replacing a complex inner expression with a single variable to simplify the integral.
