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Calculus · Definite-Integrals

Integrate k^(1/3) from 1 to 100

\int_{1}^{100} \sqrt[3]{k}\, dk

Step by step

  1. \int_{1}^{100} \sqrt[3]{k}\, dk

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

  2. \int \sqrt[3]{k}\, dk = \frac{3 k^{\frac{4}{3}}}{4}

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

  3. F(100) - F(1) = \left(75 \cdot 10^{\frac{2}{3}}\right) - \left(\frac{3}{4}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = - \frac{3}{4} + 75 \cdot 10^{\frac{2}{3}} \approx 347.37

    Simplify.

Reveal the answer
- \frac{3}{4} + 75 \cdot 10^{\frac{2}{3}}