Area & Volume by Integration Calculator
Integral applications: area & volume S = ∫|f − g| dx, V = π∫f² dx
Choose a problem. The tool finds the bounds from the intersection points when you leave them blank, checks signs to remove the absolute value, finds the antiderivative, substitutes the bounds and gives the exact result with a decimal value.
The calculator above applies definite integrals to compute the area of a region between curves and the volume of a solid of revolution around the x-axis.
Formulas used
S = ∫ₐᵇ |f(x) − g(x)| dx
V = π ∫ₐᵇ f²(x) dx
- Split the integral at the points where f(x) − g(x) changes sign.
Worked example
Area under y = x² from 0 to 3:
S = ∫₀³ x² dx = 9
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Type the functions and the bounds a and b.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.