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Definite integrals

Area under a curve and the fundamental theorem of calculus.

A definite integral is the signed area between the curve and the axis on an interval. Find an antiderivative F, then compute F(b) − F(a) — the fundamental theorem of calculus. The shaded region in the graph is the area being computed.

වැඩ කළ උදාහරණය: integrate x^2 dx from 0 to 1

Calculus · Definite-Integrals

Integrate x^2 from 0 to 1

\int_{0}^{1} x^{2}\, dx

පියවරෙන් පියවර

  1. \int_{0}^{1} x^{2}\, dx

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int x^{2}\, dx = \frac{x^{3}}{3}

    Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

  3. F(1) - F(0) = \left(\frac{1}{3}\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{1}{3}

    Simplify.

උත්තරය හෙළි කරන්න
\frac{1}{3}

ඔයාගේම උත්සහ කරන්න

තවත් Calculus

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