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Calculus · Definite-Integrals

Integrate x^2 from 0 to 3

\int_{0}^{3} x^{2}\, dx

Step by step

  1. \int_{0}^{3} 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(3) - F(0) = \left(9\right) - \left(0\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = 9

    Simplify.

Reveal the answer
9