Calculate Definite & Indefinite Integrals
Find antiderivatives and area under curves with step-by-step solutions. Supports definite integrals with bounds and indefinite integrals with the constant of integration.
How It Works
∫xⁿ dx = xⁿ⁺¹/(n+1) + CThe power rule for integration is the reverse of the derivative power rule. For ∫xⁿ dx, increase the exponent by 1 and divide by the new exponent. Add + C for indefinite integrals (the constant of integration).
Quick Tips
Power Rule
∫xⁿ dx = xⁿ⁺¹/(n+1) + C — increase exponent, divide by new exponent.
Constant
∫c dx = cx + C — a constant integrates to a linear term.
Definite Integral
∫[a,b] f(x)dx = F(b) - F(a) — the area under the curve between a and b.
+C
Always add + C for indefinite integrals — the antiderivative is not unique.
Step-by-Step Instructions
- 1Enter your function in polynomial form (e.g., 3x^2 + 2x - 5).
- 2Choose Indefinite (general antiderivative) or Definite (area under curve).
- 3For definite integrals, enter the lower and upper bounds.
- 4Click Calculate to see the integral and step-by-step solution.
Frequently Asked Questions
What is the difference between definite and indefinite integrals?▼
An indefinite integral gives you the general antiderivative (+ C). A definite integral calculates the exact area under the curve between two bounds, giving a numerical result.
Why do we add + C?▼
The derivative of any constant is 0, so the antiderivative of a function is not unique — it could differ by a constant. + C represents this unknown constant.
What does the area under a curve represent?▼
It represents the accumulated quantity. In physics, area under a velocity-time graph = distance. In economics, area under a demand curve = consumer surplus.