doomath Calculator
Definite & Indefinite Integral Calculator
Evaluate definite and indefinite integrals, compute exact antiderivatives using the Fundamental Theorem of Calculus, and compare numerical Riemann approximations.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSDefinite & Indefinite Integral Calculator — Mathematical Derivation & Steps
2 StepsSequential Calculation Breakdown
1
Antiderivative
Integrate each polynomial term.
2
Evaluate bounds
Subtract the lower-bound value from the upper-bound value.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Definite & Indefinite Integral Calculator
Evaluate definite and indefinite integrals, compute exact antiderivatives using the Fundamental Theorem of Calculus, and compare numerical Riemann approximations.
01Set inputsChoose values, units and assumptions.
02Apply the model∫ [c₂x² + c₁x + c₀] dx = (c₂/3)x³ + (c₁/2)x² + c₀x + C; Definite: F(b) - F(a)
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Input polynomial integrand coefficients and integration boundaries [a, b]. The calculator determines the symbolic antiderivative and calculates the net signed area under the curve.
Formula & method
∫ [c₂x² + c₁x + c₀] dx = (c₂/3)x³ + (c₁/2)x² + c₀x + C; Definite: F(b) - F(a)
Assumptions & notes
- The Fundamental Theorem of Calculus links differentiation and integration.
- Simpson's rule provides a quadratic parabolic approximation for numerical quadratures.
- The average function value over [a, b] is given by (1 / (b - a)) ∫ f(x)dx.