The Fundamental Theorem of Calculus

This integral calculator evaluates definite integrals exactly using the fundamental theorem of calculus: for a function with antiderivative F, the integral from a to b equals F(b) − F(a). Each supported function is paired with its exact antiderivative, so no Riemann sums or numerical quadrature are involved.

Signed Area

The definite integral measures signed area — regions below the x-axis count as negative. The shaded chart shows the curve between the two limits, and the result equals the net (signed) area under it.

Average Value

The average value of a continuous function on an interval equals the integral divided by the interval length. It answers questions like \"what constant would give the same total area?\" and is exact here because the integral itself is exact.