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Calculus · Definite-Integrals

Integrate k^(-5/3) from 1 to oo

\int_{1}^{\infty} \frac{1}{k^{\frac{5}{3}}}\, dk

Step by step

  1. \int_{1}^{\infty} \frac{1}{k^{\frac{5}{3}}}\, dk

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

  2. \int \frac{1}{k^{\frac{5}{3}}}\, dk = - \frac{3}{2 k^{\frac{2}{3}}}

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

  3. F(\infty) - F(1) = \left(0\right) - \left(- \frac{3}{2}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \frac{3}{2}

    Simplify.

Reveal the answer
\frac{3}{2}