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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.

ឧទាហរណ៍​ដែល​បាន​ធ្វើ: integrate x^2 dx from 0 to 1

Calculus · Definite-Integrals

Integrate x^2 from 0 to 1

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

ជំហាន​ដោយ​ជំហាន

  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.

បង្ហាញ​ចម្លើយ
\frac{1}{3}

ព្យាយាម​របស់​អ្នក​ផ្ទាល់

បន្ថែម​ទៀត​ក្នុង Calculus

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